I don't like the idea that, I can modify my source file in any way when debugger is running. I hate accidents. Pausing it and make changes, at least is a deliberate action.
You can always make a quick garbage loop above your breakpoint during the pause. And you just drag the arrow above the loop and it will just execute that garbage. And just let the loop run from time to time, and you can avoid timeout.
Of course, if VS does this, they have more freedom to do just like you said.
I think the feature should be called, Zero TimeOut Breakpoint. The objective is basically break the debugger without getting TimeOut. And that would be a more precise description of what you want.