3 of my All-on-4 implants were rejected 4 weeks after surgery. Will it happen to the rest? Will the replaced implants be OK?

This common problem is one of many reasons good teeth should not be extracted for all on four implants.My crystal ball is broken but the majority of patients who lose implants do eventually heal.

Successful implant therapy is possible in patients receiving Autoimmune therapy for Arthritis. The Dentist needs to explain you the possibility of osteonecrosis development. An individual risk assessment is essential, taking the primary disease with the medication and further wound-healing-compromising diseases and medications into account. If possible, bone augmentations should be avoided, and a perioperative antimicrobiological prophylaxis is strongly recommended in these patients.
Avoid Immediate Loading and Bone Grafting...!!
Prefer to have more number of Implants. Healing Period of atleast 6 Months and then Loading of Implants. Remember : All-on-4 NONE on 3.

While nothing is ever 100%, adding or replacing implants after rejection are usually successful. One of the common reasons is that a typical All on Four process involves removing teeth on the same day as placing implants. Revisions are usually in completely healed sites, so it is much easier to contain any bacterial contamination and the bone stability is better (placing an implant into a solid block instead of the "swiss cheese" bone from the tooth extractions). Since one of the implants worked, it should mean that success is possible and likely.

It’s a simplistic answer, and likely an incorrect one as well,  to say that you shouldn’t have had implants placed..... there’s a reason that you considered the All-on-4 in the first place, likely your teeth were in poor condition and you were looking for full arch options. The All-on-4, when done correctly, is far and away the best option to replace a full arch of teeth.
While your autoimmune condition may have played a part in the failure of these implants, it’s impossible to truly determine the cause of failure without seeing the full picture.
The success rate of the All-on-4 is as a matter of routine in the range of 97-99%. This is verifiable through studies that date back to 1990. Your autoimmune condition may have lowered the success rate somewhat, but I’d still expect a success rate in the range of >90%.
There are multiple reasons why implants fail as part of the All-on-4 procedure and it almost always points back to the provider completing the procedure. I wish I could say that your experience is uncommmon, but as the All-on-4 becomes more mainstream, many dentists and “specialists” are jumping into providing treatment with both feet without having a true understanding of what they’re doing.... As an Oral Surgeon, I am seeing more and more salvage cases; these are cases that were initially completed by another provider and are now needing to be redone.
While I do not want to make accusations without having the full picture, you may want to consider getting a 2nd opinion in an effort to better understand what happened, and to avoid a repeat occurrence.