Not being tremendously into FIFA and only playing it sparingly (usually at the same time as playing Football Manager or a slow-paced PC game like the X series where you could have very little to do for 5-10 minutes but stare at the computer screen as you fly around space), my longest career is a measly 3 seasons long - started at Man Utd and managed to work my way up into getting a first team spot, moved to St Etienne as captain because I wanted more first team action, didn't like being the best player at the club by quite some distance and feeling like I had to be involved in everything all the time for the club to be remotely successful (St Etienne were rubbish - virtually every goal they scored, I either got it or had the assist. They very rarely posed any threat to other teams, even the worse ones in the league, if I wasn't playing too well), so moved to Spurs where I could happily rely on my teammates to be competent and able to grind out a result even if I wasn't at my best.
Although I didn't play it that much, I did find the advancement through the ranks happened too quickly, and I can see why you might only stick at a career for 3-4 seasons; after all, I was far from the best but even I started out as a reserve in Man Utd and by the end of the first season I was getting offers for first team roles at some of the biggest clubs in Europe but (foolishly) chose to captain St Etienne for a change of pace; if you're good at the game, unlike myself, I can imagine that this would only be accelerated (perhaps you'd be getting key player or captaincy offers at these clubs)