The bookmakers have Silva as the favourite to be the next Premier League boss sacked and, while Everton have historically given their managers time, a fifth consecutive defeat would surely push the Portuguese closer to the exit door.
Not since October 2005 have Everton suffered a longer top-flight losing run than the four-game streak they are currently on, with that leaving them in the relegation zone having only picked up seven points from their opening eight games.
It is a far cry from the level of expectation which surrounded the club ahead of the new season; the signings of Moise Kean, Alex Iwobi and Fabian Delph led to predictions of a top-six push which now look to be wildly optimistic.
The Toffees surely have enough quality to ensure that they will not be dragged into a relegation dogfight, but the main question right now appears to be whether Silva is the right man to get that quality out of the team.
The visit of West Ham could be a perfect opportunity to claim just their third win of the season, with Everton having registered more Premier League victories (25) and scored more Premier League goals (83) against the Hammers than they have against any other side in the competition.
However, Manuel Pellegrini's current crop have bucked that trend in recent clashes, winning two of the last three Premier League meetings - as many victories as they had managed in their previous 22 before that.
Indeed, the Hammers could win consecutive top-flight away games against Everton for the first time since March 1930, and many will be backing them as favourites considering their confident start to the season.
Just two points separate them from the top four after eight games, while the fact that they currently sit above Tottenham Hotspur and Manchester United in the standings has raised hope that they could be challenging for the same top-six berth that Everton were tipped to claim.
West Ham will view their next four games - against Everton, Sheffield United, Newcastle United and Burnley - as winnable fixtures, although they did go into the international break off the back of a poor run of form which included a 4-0 drubbing at the hands of League One Oxford United.
In general, though, their away form has been decent and they have not tasted a Premier League defeat on the road since April - a six-game streak which is their longest for more than a decade.
Everton Premier League form: LWLLLL
Everton form (all competitions): WLLWLL
West Ham Premier League form: WWDWDL
West Ham form (all competitions): WDWLDL
Many of Everton's new signings are yet to really kickstart their careers at the club, but Jean-Philippe Gbamin has got off to the slowest start of the summer arrivals due to injury.
The Toffees received more bad news earlier this week when he was ruled out for another three months, keeping him sidelined until January.
Captain Seamus Coleman will also miss this match through suspension following his red card against Burnley last time out, while Delph is an injury doubt due to a hamstring strain.
Everton possible starting lineup:
Pickford; Sidibe, Keane, Mina, Digne; Gomes, Delph; Richarlison, Sigurdsson, Iwobi; Kean
West Ham possible starting lineup:
Jimenez; Fredericks, Diop, Ogbonna, Cresswell; Yarmolenko, Noble, Rice, Lanzini, Anderson; Haller
We say: Everton 1-1 West Ham
Everton will be desperate to stop the rot on their return to league action after the international break, but they are coming up against a West Ham team with plenty of attacking quality. We can see the hosts ending their losing streak, but still being forced to wait for another victory.