The Hammers were thrashed 5-0 in the FA Cup by Manchester City at the London Stadium last time out.
The humiliating defeat follows an embarrassing early exit from the Europa League to Romanian minnows Astra during qualifying, a 4-1 defeat in the quarter-final of the EFL Cup to Manchester United and a torrid season in the Premier League which has Bilic's side sitting 13th in the table at the halfway stage.
Most supporters point the finger of blame at broken promises from the West Ham board over transfer spending following the big move to the Olympic Stadium.
West Ham United manager Slaven Bilic looks dejected
But some are beginning to turn on the Croatian, who last term led the East Londoners to their best points tally - and first positive goal difference - since 1986.
Bilic is second favourite to be the next Premier League manager to lose his job and former Hammers defender Matt Upson told BBC Final Score he fears they have lost their identity this term.
"Last season when you'd watch them at Upton Park they had that real intensity about their play under Bilic and real desire and that made them dangerous," Upson told BBC Final Score.
Matthew Upson in his West Ham playing days
"This season they've never really had that.
"They haven't got that as a team and they've lost that identity."
As well as the big move to their new 60,000 seater Olympic Stadium home, West Ham's season has been beset by problems from a poor summer of recruitment to injuries.
Bilic has been linked with a number of players in the January transfer window but it remains to be seen whether the club can land any of its rumoured targets.