Are you using alarm to time-out SQL queries? That will only work if you have "safe signals" turned off. This makes the signals... unsafe. I don't recall the exact errors that we ran into due to that, but yours certainly seem similar.
Empirical statistics suggest that about 10% of such firings of SIGALRM will result in the Perl interpreter becoming, shall we say, "unhappy". The safest thing is to just force the process to exit quickly after an unsafe signal gets processed.
I think Perl actually does things with "safe signals" that actually prevents a signal from interrupting an I/O operation. If so, that is quite unfortunate. If not, it might be fairly easy to build a patched version of the DBD module you are using such that interrupted I/O requests don't get restarted.
It is certainly very unfortunate that Perl can't safely time-out a DB operation.