Hi,
So if you create a new UPS shipping method and don't enter anything in its settings and just save it, do you still have the same problem ? If not, could you add the information option per option, and between each option, save it ?
That way, if you get the error at some point, we would be able to understand which setting is the problem.
That would help understand what's going on.
Also, usually when such an error happens, your server should log in the PHP error log the real error message with the reason of the crash and the file and line where it crashed. So if you could look in your PHP error log for a "Fatal error" message, that would help us understand what's going on if you find one.
If you don't know where to get access to the PHP error log, you might have to ask your hosting support.