Could it be that there is some kind of time limit for running Perl scripts on the server?

Sure, I'm assuming mod_cgi (or equivalent) timeout (timeout)

Hope that somebody has the solution.

Disable timelimits. Maybe launch process in background, Proc::Background, Highlander: one instance at a time (Oct 00), Watching long processes through CGI (Aug 02), Re: ERROR on CGI script:The timeout specified has expired