An update to the php.ini or .htaccess file to set the session.gc_maxlifetime is probably the best solution.
You could do it in the php code itself with:
But you would probably have to put that on every admin page to make sure it didn't get reset to the default. One option might be to add it to your connection include or another include that might already be on all of your pages.
Another option is to use a standard cookie to store and retrieve session data. That would work for more long-term session persistence, but it would also take a bit more work.