We are on mod_perl 1.x as well and we ran into a very similar problem. Code that was otherwise working well would throw the same UNDEFINED SUBROUTINE, MyPackage::handler called. It was plaguing us for months on many different production servers on many different clients' servers.

When I finally tracked it down, it was a block of code that was writing a Data::Dumper output to an Apache::Session::File object. When the session was written, we'd have this same issue, no error message except that one put in the logs.

In fact, further requests that hit the same apache subprocess would also have the same error.