It seems to become apparent when a script gets to a certain size and complexity, and can exhibit the reboot every alternate save. The strange thing for me is that despite getting its nickers in a twist it usually still keeps track of things during the reboot such that it still completes the save most of the time. But not all the time. So the important point is whether it pops up the 'Saved OK' window after the reboot, otherwise it may not have actually saved it ok.
I recommend always doing a 'select all' and 'copy' before doing a save.
If the 'save' gets lost without completing or rebooting, your edit window and buttons can become unresponsive, in which case the best way to nudge things back to life without rebooting is to do a browser 'back', then browser 'forward' to your edit page again, which should hopefully then become active again. The only way to be certain of correct saves is to do an 'edit' (to download from the ESP) and check if your last edits did save or not. If not, 'paste' back your contents and try saving them again... and now might be a good time to also 'paste' your latest edits to a text file for safe-keeping on your computer. I've mainly used Firefox simply because it is independant of any big corporate, but I get the same 'reboot during saves' problem with Chrome.
ESP_Basic is not perfect, but don't let that distract you from how good it actually is.