Keep, for now.
I predicted we will be in a relegation battle before the season began despite the new signings and I still do. We made good signings despite their age but even so we needed to, our form at the end of last season was awful and had the season been two or three games longer we would have gone down - we had little quality but Ralph also showed he couldn't turn it around. This season we have picked up points against a poor Leeds and Leicester side and a Chelsea side that is in transition. We've been poor in the last two games against opposition that shouldn't have been tough to get at least a point from - especially Villa which was one of the worst performances I've seen in ages.
Then you look at the selections - Moi is not good enough for the Premier League. He just isn't. He might work hard and be OK technically but he really doesn't do what an Attacking Midfielder should do, and that is create chances... or even score them. And yet Ralph continues to select him over Aribo, Stu and Edozie. We also have Adams up front as our main goal threat because we didn't bring in a properly good striker and currently have Diallo in midfield alongside JWP because, apparently, AMN isn't ready.
Personally I'm conflicted about sacking him now. I wanted him gone in the summer and was surprised the powers that be kept faith in him (as it seems were some of the players) but with the new signings I was going to see how he did until Christmas. We've started...averagely. For me I would keep him for now and see how he does over the next few games... especially Everton who we REALLY should be trying to beat. If we can't beat Everton at home then I would be seriously concerned.
Our saving grace this season is a long break for the WC and the January transfer window that we already know we will have spending money in (Gakpo money if that was ever serious). It is for this reason that I believe if we are going to bring in a new manager, it has to be done by then, to give the new manager a while to get used to (most of) the players during the break and decide where we need to strengthen in January (ATTACK!!!).
We have Everton, West Ham, Bournemouth and Palace (alongside tougher fixtures... and possibly the rearranged Brentford game) between now and the WC - those will be the big decider as to whether to keep Ralph. If we're not on 15+ points by then he needs to go - and even then only 15 points going in to the second half of the season would leave a lot on for the new man.