Lampard has lost six of his seven league games since taking charge of the club at the end of January and is struggling to keep them above the relegation zone.
They sit just a point above 18th placed Burnley following their 3-2 defeat at Turf Moor and are edging ever closer to the dreaded drop zone.
A certain section of Everton fans have already turned against Lampard due to his failure to lift his side and there are now question marks over his future at Goodison Park.
But it has been claimed that the Everton board do not feel that changing managers at this stage is going to make a massive difference.
The board are concerned about the way Everton are unravelling and are desperate to avoid relegation.
And despite their stance, Lampard is still not sure to last the season at Everton if their current form continues.
Everton have already been reeling financially due to overspending in previous years and relegation could further drill a hole in their pockets.
Only a few Everton players have relegation clauses in their contracts, which would reduce their wages if they drop down to the Championship.
