The cause is you probably have bugs in your code that are hidden by the additional delays in debug.
The solution would be to systematically track down what the bug is by looking at what is happening vs what is not happening, checking appropriate assumptions, and instrumenting your code with sufficient checks and error reporting mechanisms.
Hard to understand what's actually happening here. Your title says "does not work if not debugging" but your text only reports an error that would occur while debugging (i.e. "some variables become unresponsive"). Or does rebooting the board mean you're no longer debugging even though you're still connected with j-link? More clarity might help.
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