I've always been in the "shouldn't have been appointed in the first case, but give him time" camp.
Pre-RWC, I was unhappy and unconvinced, but he had to be allowed the RWC itself.
During the RWC he reached par, and did so in unspectacular and uninteresting form - but it was enough that I wasn't calling for his head; but had him as "up for review after the 2024-25 season"
After the 2024 6N, he was in the ball-park of par to slight under-acheivement, with 3 dross performances, and 2 good ones; those 2 were enough to think he was still on target for "up for review after the 2024-25 season"
After the 2024 SIs, he had narrow losses to NZ (so, about par), but the performances were far from encouraging, but... he might still come good.
He needs to go 2 from 4 this Autumn, and currently, he can only do that by beating South Africa, whilst showing no signs of being capable of working out how.
If I were the RFU, I'd be dusting out the little black book today, and deciding on who to appoint in charge of recruitment for a new HC; but I'd hold fire until this time next week. If he does get the win against SA (and Japan) then he gets the 6N to turn things around; if not, then he gets the 6N as caretaker whilst we identify and negotiate with his replacement. Meaning that the actual hire comes in the summer, when everything should be more reasonable from a release point of view (and as part of that, a "******* off the current employer" point of view).
The only candidate I would consider from the Prem to take the role would be Mark McCall, but I doubt he'd be interested.
Ideally, the candidate should have experienced success as head coach at club level, and experience (preferably successful) as head coach internationally. I would assume any current tier 1 international coach is unavailable mid-cycle.
Off the top of my head, the short list could look something like:
Mark McCall
Jake White
Michael Cheika
Ronan O'Gara
John Mitchell (would need a longer caretaker role beforehand)