Is there any was where BP can triggers when BP is stuck due to unexpected message pop ups or applications is not responding or process is taking longer than expected.
Newer versions of BP have a 'global timeout' in application manager you can set for applications that do not respond. If your version has this, you can see it in application modeller when you select the top element in the left hand tree.
Blue Prism has relatively new feature where a timeout can be added to application modeller. It is in all versions of v6 and the last few versions of v5 (check the release notes to find out which versions of 5 has it in).