Quite possibly yes. Though I don't think we will lose the next 4, we'll bumble through 1, maybe 2 of those. The year ends with Liverpool and Man City. If he's not gone by then do they bring in a new man to take an absolute hiding from them? You'd assume not generally. So he'll get 6 games. We play Jan 4th then Jan 15th, so a solid 11 days for a new guy to get a look at the team, try and instill something, and identify where they want improvements before a home game against Palace.
I don't think we'll do great in the coming games, but I also don't think others will either. Saints next 4 looks a guaranteed 0 points. If they're not keen on pulling the trigger when they've seen the turgid football and had nice international breaks to bring someone new in, I don't think they'll do it on the back of some poor results even now. It'll probably take 4 games for us to drop into that mire, and then I think they might be looking for someone new but won't want them to have the baptism of fire that comes with our Christmas/New year fixtures. Although I'm looking at it from the point of when I think they'll want to appoint someone, and I suppose he can be sacked weeks before someone is appointed, so on that front it's a possibility. I'm looking at it more as though I don't think we'll have someone new before January.