Do my games in the GoKGS get deleted after some time?
The mentioned list of games is the list that is displayed in your profile. It only displays games from the last 180 days and only the games in the last 180 days are considered for the rank graph. You can review these games directly (right click on a game in the list --> Load in ... or Load in (P)). 

All games (even these which are older than 180 days) are listed in the archive. There you can access all games which are not private. Unlike the games which not older than 180 days you must download them first to review them. I just don't know if private games are just not accessible in the archive but accessible on demand or are even deleted.