I can't be sure without seeing the code for FRHWebDB::Session, but it looks to me like you have a scoping problem. You've made your session variable global, so it doesn't go out of scope until Perl shuts down. You should try making it lexically scoped (my) and let it go out of scope at the end of your CGI. Or you can do a quick fix by setting it to undef at the end.
By the way, you don't need to explicitly exit at the end of a CGI, and it hurts portability to mod_perl, so leave that out.