Non Missions Specific Characters follow the standard SR4A guidelines for improving...
Aka, treat them very well, and the GM may (at his discretion and if he feels it's warranted), raise their loyalty. If you go out of your way to work on your Contacts during play, you may want to ask your Gamemaster at the end of the session if you managed to improve your loyalty at all (Be polite, and don't bug him about it though). There's a lot of wrap up to do, and at a con it's easy to forget stuff, especially the stuff that falls outside of Missions paperwork. So a nice, simple, friendly reminder may be helpful for him to go "Oh, right!". But just remember you won;t always raise their rating up every session.
Bull