Instead of simply crashing, alert the user to a monitor hardware malfunction
I recently found out through a very circuitous process that my monitor is failing. But in this process, instead of alerting me to any issue, the drivers would crash and the icon would disappear from my system tray, making me think your software was malfunctioning. Instead, such a crash should be caught with exception handling, and then alert the user there is a hardware malfunction.
We already try to gracefully restart whenever possible. You might encounter an unforeseen case not handled properly which would need crash dumps to be investigated.