They appointed Poch in the hope he could achieve regular CL football on a budget dwarfed by our competitors. He did that consistently and ahead of schedule.
Poch's aspirations then grew, but Levy's didn't, so now we're in the situation we find ourselves in today.
So I think Levy is now in a quandry.
He realises his best bet is hoping Poch turns things around and gets us fighting in the top 6 or 7 for the next few seasons while a gradual rebuild gets underway.
I think he realises the cost of building this team into immediate CL contenders again outweighs the cost of missing out on top 4.
Therefore, he'll hold on to Poch as long as possible.
He knows there's no chance of attracting the likes of Pep, Klopp ,Mourinho or any other serial winners, so I think he's written off this season and the next couple as well.
In fact, that could explain Pochs current demeanour. He knows he's safe.