Debugging asp.net suddenly stops

Have you set your debugger to break on all exceptions, not just unhandled exceptions?

Debug -> Exceptions -> Check the "Thrown" box for everything (or at least just Common Language Runtime Exceptions). If an exception is thrown during debugging, on any thread, this should cause the debugger to highlight and break on the "thrower".

Another thing to try, is to reset all your IDE settings. I've had various odd behaviours before where settings got corrupted and the IDE stopped behaving sensibly: Tools -> Import and Export Settings -> Reset All Settings.

In addition to Daniel Dyson's answer - if you "pause" as he suggests (once the debugging has "stopped"), open the "Threads" debug window. Are there any threads showing that have an entry in the "location column". If so, this is probably your code executing. Click on each in turn. Can you account for what each thread is doing, or does this shed any light on this odd behaviour?

Have you tried hitting the Pause || button? This will pause the debugger wherever it is executing, so if you are in an infinite loop outside of your try catch block, you will be able to find out where.