Certain things in the game also raise your SeeD level, such as not messing up on the mission on President Deling's train.

I think my SeeD rank went down because I crashed my car into the train once.

From what I have seen, it's impossible to maintain a level "A" SeeD rank unless you follow the storyline completely without stopping to level up, play card games, sidequests, etc. Basically, don't bother getting you SeeD rank to the max.