First of all you can look into the bug trackers for LWP::UserAgent on CPAN and for perl, perhaps that error is already known.

Second step is to check versions: do you run the latest maintainance release (5.8.8) of perl? If no, consider upgrading; there are reasons that 5.8.8 was released, and the most prominent is: bug fixes.

Finally you can start a debugger (like gdb) or a memory debugger (like valgrind) and try to gather some information on where that segmentation fault occurs (perl core, or a library?), perhaps even build a perl with debugging symbols to find out more.