Star player Dimitri Payet demanded a move back to Marseille in January and the club has flirted with relegation while also being dumped out of the Europa League, FA Cup and EFL Cup in embarrassing fashion.
Supporters have been disillusioned and despite the fact the Hammers have gone three unbeaten, they still need at least one more win to more or less guarantee survival.
But just when Bilic looks to be winning one battle, he could face another one off the pitch should Everton boss Ronald Koeman come knocking with moves for three key Hammers players this summer.
West Ham United's Manuel Lanzini celebrates
The little Argentine has been one of the club's only consistent performers this season and has eased the pain of losing Payet with his creativity.
"Of course I have seen Everton and they are a very good team with very good players,” Lanzini told whufc.com.
"Ronald Koeman has a good striker in Romelu Lukaku, who is an amazing player... they also have Ross Barkley, who is a very good player. I don’t think he is thinking about the pressure people are putting on him, because there was a lot of pressure on him last week and he played really well against Hull City.
“He has a good touch, good finishing and good recovery, so he is a very good player. I don’t think the pressure is a bad thing for him."
Barkley has been linked with a move away from Goodison Park this summer with Tottenham Hotspur said to be interested, and Lanzini could be the ideal replacement for him.
West Ham United's Cheikhou Kouyate
One of if not the most important players at West Ham, Kouyate is hugely popular with fans and teammates alike.
Supporters have been hugely frustrated with Bilic's use of the Senegal star this season as he has been deployed at right back and in central defence rather than in the middle of the park where he is one of the best in the Premier League.
Kouyate recently made it clear he was not happy at being played out of position and he has been linked with a move to Spurs in the past.
Everton are a club on the up and are a tier above the Hammers in that respect so a move to Goodison might prove tempting for Kouyate.
Enner Valencia is on loan with the Toffees from West Ham
Everton have first option on making Valencia's move permanent from East London this summer.
The Ecuadorian has scored three goals in 19 appearances, mostly as sub, but has enjoyed some eye-catching performances, most notably against Southampton in a 3-0 win back in January.
The Hammers are keen to recover as much as the £12.5 million they paid to sign Valencia but Everton could well get themselves a bit of a bargain for anything under £10m.