I think FSG are pretty set on Rodgers having another season, and from their perspective (as Darcus pointed out) they probably don't see him as doing THAT badly. They don't seem fussed about making Liverpool a big club (e.g. Stadium), they aren't fussed about getting top quality (e.g. any player we have bought under Rodgers pretty much), they don't turn up to games that mean a lot to the fans, etc etc.
Rodgers got us close'ish to 4th place without ever being in any danger of actually achieving it, is that about enough to keep the brand alive, probably. Do they care about anything else? Seemingly not. To anyone with footballing sense and passion for the club it is very clear this was a massive failure for him (and everyone else involved with the club) in my opinion, but this isn't were their decision drivers come from so I think it will play little part. They know they can give Rodgers another year before the fans start boycotting anything so that's what they'll do, keep their man who tows the party line until it is impossible to keep him, i.e. next christmas or next season's end where he obviously won't get top 4 again.
At this point the one manager who we might have got (if he's willing to take Fenerbahce!) who would be quite an exciting appointment, though not the definite saviour some make him out to be, will be in a long term deal and we will poach the gary monk of next season. At which point the merry go round starts again except this time we are EVEN FURTHER BEHIND, and are unlikely to strike Suarez type gold a second time so soon after he so richly rewarded us with goals, performances, and the second juiciest transfer budget in the league.
