The team will fix this bug with the next update (version 145).

A couple notes:

• Some users say that reinstalling Firefox fixed this issue for them
• Once the fix is released, you may still see an issue on your next immediate launch. However once you update your search engines again, the problem should no longer occur
• In the meantime, users can also try deleting all their custom engines and re-adding them. This may resolve the issue for you as well without an update.

How do I delete search engines on Firefox in iOS?

In Settings -> Search. If you've added it, you can remove it too.

That’s strange. I’d check if Firefox recently updated, as updates can sometimes reset default settings. Also make sure Google isn’t set as the default in iOS system settings or being enforced by a profile. If it keeps switching back, try reinstalling Firefox that usually fixes random setting issues like this.