The Gunners slumped to a 4-3 home defeat against Liverpool yesterday.
And the Emirates faithful are becoming increasingly frustrated with the Frenchman's lack of action in the transfer market.
However, Neville claims the experienced chief will be missed when he does eventually leave Arsenal.
He told Sky: "I am sure when Arsene Wenger is not here, there will be a massive amount of admiration for what he has achieved at this football club.
"I would advocate him staying on because it feels like we have new managers every 10 minutes and he is a stalwart.
"You look at what he has achieved - he is the most successful manager in their history.
"Unfortunately the shame of modern football as it is, we don't appreciate stability and continuity as much as we should.
"When you sign five or six players and sack your manager, it's almost like fans are invigorated again."
