I am having a site coded for me and I noticed that I get logged off of his script about every 20 minutes or so.

He told me it has nothing to do with his script. He said the server logs everyone off every 20 minutes.

Is that possible?

yes :)
for example in php you can have (at least) 3 settings in php.ini that might be responsible for such behavior:

session.cookie_lifetime
session.cache_expire
session.gc_maxlifetime

read http://php.net/manual/en/ref.session.php
for more info

Thank you. I learn something every day and that was my lesson today. :-)