A simple option could have been to use a Switch Item with an Expire Property. When the door opens, set that Switch Item to 'ON' and initialize a Number Item to be count how many checks will be done. When the Switch Item expires, execute a script which checks if the door is still opened. If it is not, that script ends. Otherwise, it increases the Item Number. If that Item Number is lower than the maximum checks to be done (your threshold), Set back the Switch Item to 'ON'. Otherwise, send the notification email.

Another option (just for fun) relies on a DSL Script with a lamdba expression which creates a Timer calling itself recursively until the door is closed or your threshold is reached. That DLS Script must be called when the Door opens.

Here after a Number Item SensorGarageDoor_Duration is used to count the number of checks: The Item SensorGarageDoor_OpenClose is the state of the Sensor on the Door.

val int treshold = 3
var int attempt = 0

// Define a Lambda Expression to check if the Door is open and if not,
// call itself after 15 minutes to check again until a treshold of calls is reached
val Functions$Function1 Monitor = [	Functions$Function1 recursive |
	if (SensorGarageDoor_OpenClose.state == OPEN) {
		logInfo("default.rules", "Monitor Opened Door")
		createTimerWithArgument(now.plusMinutes(15), recursive, [ Functions$Function1 callMonitor |
				var int duration = (SensorGarageDoor_Duration.state as Number).intValue + 1
				SensorGarageDoor_Duration.sendCommand(duration)
				logInfo("default.rules", "Garage Opened since " + duration.toString + " cycle(s)")
				if (duration == treshold) {
					logInfo("default.rules", "Notify by email that Garage still Opened after " + duration.toString + " cycles")
					val mailActions = getActions("mail", "your smtp binding")
					val success = mailActions.sendMail("your from", "your subject", "your message")
				} else if (duration < treshold) {
					callMonitor.apply(callMonitor)
				}
			])
	} else {
		logInfo("default.rules", "Stop monitoring Door")
	}
	true]
	
if (SensorGarageDoor_Duration.state != NULL) {
	attempt = (SensorGarageDoor_Duration.state as Number).intValue
} else {
	attempt = treshold
}

if (attempt >= treshold) {
	logInfo("default.rules", "Request for monitoring Opened Door")
	SensorGarageDoor_Duration.sendCommand(0)
	Monitor.apply(Monitor)
} else {
	logInfo("default.rules", "New request for monitoring Opened Door ignored")
}

One of the trick is to pass the Lambda Expression as parameter to the Timer (Created with createTimerWithArgument). Indeed, a Timer may not call a "Global" Lambda Expression. To get a Lambda Expression as parameter, this parameter must be defined as Functions$FunctionX (where X is the amount of parameters of the Lambda Expression). In my sample above, my Lambda as one parameter which is itself, to be passed to the Trigger (So, it is typed Functions$Function1).
You must type explicitly the parameters as Functions$Function1 to be able to use the method "apply()".

Openhabian's backup solution 'Amanda' didn't convince me to automate such a backup. So I wrote my own backup script and scheduled it with a cron job.

First, create a shared folder named "backups" on your Synology via Control Panel > Shared Folder > Create:

Next, create a user account named "backup" via Control Panel > User > Create:

Grant that account write access on the shared folder "backups" via Control Panel > User > backup > Edit > Read/Write

The Synology part being ready, move now to openhabian, on the RPI, using a ssh console (E.g.: Putty) to create and schedule the backup script. Most parts will have to be done as 'root' (to make it simpler... but no safer), so type;

sudo -i

If just like me you previously tried to configure the backup with Amanda, using the command "sudo openhabian-config" and then the menu 50 > 52, a mailer daemon (exim4) was probably installed and you want now to remove it... Check if it's running (not with the command "systemctl --type=service --state=running" but) with:

sudo service --status-all

If you see a + in front of exim4, disable and remove it

sudo systemctl stop exim4
sudo systemctl disable exim4
sudo apt-get remove exim4 exim4-base exim4-config exim4-daemon-light
sudo rm -r /var/log/exim4/

You can also next uninstall and remove Amanda

sudo apt remove amanda-client
sudo apt remove amanda-server
sudo rm -r /var/lib/amanda/
sudo rm -r /etc/amanda

Now, we can start with the preparation of the backup script. Define first a mount point on your RPI. E.g.: "/mnt/backups":

mkdir /mnt/backups

Define next the shared folder of your Synology by editing the fstab file:

sudo nano /etc/fstab 

Add the line here under in that file and save your change with CTRL-o, Enter, CTRL-x:

//<ip of your Synology>/backups /mnt/backups cifs username=backup,password=<password>,uid=1000,gid=1000,vers=3.0 0 0

Attention: the network is usually not yet available when the fstab file is used to mount the drives a boot time. So this shared folder will most probably not be mounted automatically!

Create a file:

nano /home/openhabian/maintenance.sh

with the backup script here under:

#!/bin/sh

# Backup Openhab of Synology
log="/var/log/maintenance.log"

echo $(date) "Run openhab maintenance: $0" >> $log

if mountpoint -q /mnt/backups
then
echo $(date) "Synology's backups share is mounted." >> $log
else
 echo $(date) "Synology's backups share is not mounted. Try to mount as per fstab definition." >> $log
 sudo mount /mnt/backups
 sleep 3
 if mountpoint -q /mnt/backups
 then
  echo $(date) "Synology's backups share is now successfully mounted." >> $log
 else
  echo $(date) "Synology's backups share cannot be mounted." >> $log
 fi
fi

if mountpoint -q /mnt/backups
then
# Keep the 10 last backups
rm -f $(ls -1t /mnt/backups/Raspberry/openhab2-backup-* | tail -n +11)
cd $OPENHAB_HOME
sudo ./runtime/bin/backup /mnt/backups/Raspberry/openhab2-backup-"$(date +"%Y_%m_%d_%I_%M").zip" >> $log
echo $(date) "custom backups of openhab completed." >> $log
echo "-----------------------------------------------------------------" >> $log
fi

Make that script executable (for all users...)

sudo chmod a+x maintenance.sh

To run that script as root on a regular basis, you have to schedule it as root (using now sudo explicitly if you didn't type sudo -i earlier) via crontab:

sudo crontab -e

If it's the first time you run crontab, you will have to pick your prefered editor. I advice nano ;)

Select an editor. To change later, run 'select-editor'.
1. /bin/nano <---- easiest
2. /usr/bin/vim.basic
3. /usr/bin/mcedit
4. /usr/bin/vim.tiny
5. /bin/ed

Choose 1-5 [1]: 1

In crontab, add this at the end and ave that change with CTRL-o, Enter, CTRL-x:

0 1 * * * /home/openhabian/maintenance.sh

Notice: if you want to mount the shared drives at boot, which usually fails as mentioned previously as the network is not yet available when fstab is first called, you can add this in the crontab too:

@reboot sleep 300; mount -a

You can now try the script with:

sh /home/openhabian/maintenance.sh

If it works, it should also work when triggered by the cron job.

To run scripts as root is usually not recommended. But the backup script of openhab may only be run as root... We could run it with the account 'openhab', but the backup files will belongs to the user 'openhabian', making the cleanup tricky. I you really don't want to run and schedule my script as root, then the best option is to run it with the account "openhabian":

Still being is root mode (sudo -i), create the log file manually and grant access for all users:

touch /var/log/maintenance.log
chmod a+rw /var/log/maintenance.log

Authorize the user "openhabian" to execute the backup script "/usr/share/openhab2/runtime/bin/backup". To do this, you have to create a file in the /etc/sudoers.d folder. All files in that folder are used by the "sudo" command to authorize configured users to execute specified commands as root, with or without password. You MUST ABSOLUTELY edit that file with the command "visudo". This one will check that your changes are valid. If you edit that file with another editor and it contains an error, you won't be able to use the "sudo" command anymore (you will have to plug the SD card into a USB adapter on another raspberry to fix the issue or to simply delete the invalid file. USB device are automatically mounted under /media/usbxxx if you installed the package usbmount).

visudo /etc/sudoers.d/openhab

In that file, add the line here under and save your change with CTRL-o, enter, CTRL-x

# Allow openhabian user to execute the backup script
openhabian ALL=(ALL) NOPASSWD: /bin/mount, /usr/share/openhab2/runtime/bin/backup

Unschedule the script from root's crontab (remove the line added with crontab -e)

crontab -e

0 1 * * * /home/openhabian/maintenance.sh

And schedule it now within openhab's crontab (has to be done as 'openhabian'  user)

sudo -u openhabian crontab -e

And add

0 1 * * * /home/openhabian/maintenance.sh

Et voilà.

PS.: If you experience issues when mounting the remote shared folder, try to mount it interactively (using an administration account of  your Synology or an account having a password without symbols such as %, # or !)

apt install smbclient 
smbclient //<remote ip>/<shared folder> -U <user account>

You can also check the latest messages from the kernel

dmesg | tail -n10