Jol got us to Europe a few times (when we'd been out of European competition for a while) and then got sacked the moment it looked like we might miss europe.
Ramos won the only trophy of the ENIC ownership era and got sacked early the following season.
Redknapp got sacked after Chelsea won the CL, relegating us to the Europa League.
AVB should never have been employed in the first place I agree, unfortunately though Levy fell for his sexy powerpoint presentation where each new slide came in spinning around or something!... Once he was in the door though he was allowed to miss CL the first season and then sacked when it appeared he would do so the second season.
Pochettino got he sack when it looked like we might not make the CL for a 5th consecutive time (way to go on that one Levy!)
Mourinho got the sack just before a Cup Final, the one thing that history told us he was really good at negotiating successfully, because he wanted to rest his best players in midweek before the game to give us the best possible chance of winning the Cup final. Levy sacked him as he still clung to the idea that we might scrape 4th place.