One other factor to be thought about, if things don't improve: Levy/The board and whether they have backed Poch/are interested in Football success (as in Trophies and NOT just CL money from securing top 4).
We as fans will only be party to so much information being on the outside; however, within football circles it will likely be very well known whether Pochettino is a very GHod coached that reached a limit due to not being backed at the right times or whether he actually HAS been backed well but made certain decisions (re not buying certain players, putting to much faith in the wrong players etc) which are now costing him further down the line.
If it's the former, you can bet that the board will be wary of hiring an 'upgrade' to Poch who knows the PL very well as a) they'll be likely far less forgiving/provide 'PR cover' and b) will likely prove more expensive in that they will know what they want and want to be backed as such (nowhere to hide in terms of perceived dithering in transfer windows..)
If it's the latter, there will be a queue of managers only too willing to work with this squad and the promise of additional money to spend.
If things get worse, this might have a bearing on how much 'patience' the board has; much more than any notion about 'loyalty' as
@Raziel hints.
It's also in Poch's interests to turn it around, if only for his next job if he leaves us: the 'punching above our weight' narrative wont wash so easily anymore with boards of top clubs. Certainly not at Real or maybe even Man Utd, if our downturn continues. For his next job - if it's to be at a top club - he absolutely needs a trophy.
Could it be that this survival instinct alone means he'll turn it around? Here's hoping...