doubt

is it possible to become inmune to your reality checks in dreams and your stabilization?
if so, what to do to overcome this

The thing is that RCs are designed to help dispell your doubt that something so realistic can be a dream, but once you become really good at lucid dreaming you won't really need the RCs any more because you will know that you are dreaming without RCs.

Your question is kind of like this: People who are not very good at math, use calculators to verify whether they are correct in their answer to basic calculations like 6x5=30. So you would say what if the calculator stops working? Answer: it won't be a problem if you are confident in math.

A more complicated analogy is: RCs only work if you expect them to work /have confidence in them. Another thing that only works if you have confidence is overcoming stage fright in public speaking. If your question is what would I do if I lost confidence in myself while speaking in public and developed stage fright, and in that case the only answer is: you would need to regain confidence in yourself - there is no replacement for confidence, and expecting success is crucial to success in both public speaking and in lucid dreaming.

Does either of those two answer your question?

yes sir, thanks

Another thing: no single RC is reliable all the time, so it is recommended that one use a combination of several RCs just to double check. Also mindless RCs won't work as well as RCs done when one really thinks about it, really questions reality, and asks self how did I get here and what happened before that, and such.