I don't think you're going to be able to fix this without modifying CGI::Session.
Basically, what the "active statement handle" warning means is that the database connection is going away while there's a query still active which might have results which haven't been retrieved yet. Some database drivers are smart enough to recognize that a query has had all results retrieved when the last row is fetched. Others don't recognize this until you attempt to fetch a row that isn't there. You are apparently either using one which falls into the latter category (more likely) or the session table has gotten messed up such that the id you're testing with has multiple a_session records.
The reason that switching to prepare would fix this is that it allows $sth to be destroyed when it falls out of scope at the end of the sub. prepare_cached stores a second copy of the statement handle in case that same query is prepared again later; it is this second (cached) copy which is still active when your database connection goes away and triggers the warning.
A better solution, IMO, would be to continue using prepare_cached and add the line $sth->finish; immediately after my ($row) = $sth->fetchrow_array();. This will tell the database engine that you're done with the query's results even if it thinks there may still be additional rows to return.