Update 2020-09-28: Answer from Burp suite support:
Is it just me, or is this a common thing? It kinda makes my pentesting experience quite dull. The only resolution is to restart the program if you can find out how and then you lose a lot of your progress. Thanks a bunch…
What’s happening here? Well, this problem occurs after a few minutes or hours. The window seems to “break apart” and the different pieces move around as you move your mouse or …. worse… click around.
When you stop the program, it sometimes seems to corrupt the saved file and you could easily lose days of work.