I have [a] [...] script that [...] sleeps [...] If I add an ALRM signal handler, the ALRM stops working

One problem is in the man page sleep(3), at least on Linux:

Bugs

sleep() may be implemented using SIGALRM; mixing calls to alarm(2) and sleep() is a bad idea.

Using longjmp(3) from a signal handler or modifying the handling of SIGALRM while sleeping will cause undefined results.

program keeps running!!!! Any thoughts?

Multiple exclamation marks ...

Alexander