I guess due to its very nature it was impossible for it to “jump the shark” as nothing would be too absurd for Community. However, there have been a few points after which the series’ quality went downhill:
The ending of season 3, though that had more to do with Dan Harmon leaving.
Troy’s goodbye. The series arguably lost its heart afterwards. For some reason starting with 5x6, it starts to look like everyone became an empty shell of themselves. No one’s heart was in it, I tried too hard to not get that sense. Sure, it was still top-notch comedy (MeowMeowBeenz episode, VCR episode, Season 6 paintball episode und so weiter), but funny was all that was.