It will all be speculation but I have a number of thoughts:
Eddie has always wanted control of the buying and selling of players. Max allowed him to do that. The team that has just been relegated was his team, his players and his staff, not people parachuted in by a director of football.
Eddie knew we had a choice of spending money on players or infrastructure, we couldn’t do both. Rightly in my opinion, we spent it on players to try to stay in the PL
One of the reasons Eddie hasn‘t appeared to consider other roles previously could well be that no other club would give him that control.
The reality is Eddie has overseen the relegation of the most talented squad we have ever had. That squad should not have ended up in the bottom three. Eddie took us to places we never dreamed of, for which we will be forever grateful, but we cannot hide that for the past 18 months more of the performances have been poor rather than decent. We can blame the players but he has the responsibility to get that out of them. you cannot fail to view this (season) as failure.
The fact we don’t have a ready made replacement would suggest a Max wasn’t expecting this. Max has proven himself to be supportive of Eddie numerous times in the past. Most owners would have sacked him several times over given recent form. Max stood by him.
Tactically, Eddie has been found to be less brilliant than we thought at this level, his stock has dropped. Did he want to risk it declining further if he couldn’t get us back up?
My guess is Max is prepared to bank roll the club still but wanted some changes, perhaps adopting a more “first team coach” rather than old school manager. Perhaps he wanted him to off load some of the “old boys” coaching staff? They have responsibility too. Perhaps it was team or infrastructure and Eddie didn’t like it?
Regardless, we are where we are largely because of Eddie but that would have been impossible without Max’s money so I think talk of doing more to keep Eddie needs to be put in the context of we have just been relegated, poor football, his team & his players. Wenger. Went on too long, did Eddie too?