Claim denied due to non-coverage

I have a medical bill almost $2400 that my insurance is denying to pay.

My wife was covered under my insurance plan since Nov 2021. We had a blood test on 2nd Feb 2022 but later found out the claim was denied. When I called the insurance, they said she was not covered for the month of Feb. The problem is, on 2nd Feb, the provider ran my insurance and found that my wife was covered (this I verified with them lately that they indeed ran my insurance, and, I recall seeing both my name and my wife’s name popup when the provider put our insurance info).

So, basically, they dropped her from the plan for some missing documents that I was supposed to submit. And whatever the reason, I respect the decision. But you still have to let me know she was dropped right? Maybe by email or mail or sth? I got no correspondence.

Okay, even if you decide not to do let me know, you should at least show “not covered” when the provider ran you? Because my procedures that day was not an emergency, I could have waited. I added her back to the plan on March.

Now I am trying to add her back to the plan for Feb arguing that it was the insurance company’s fault since they showed her covered. So far they denied the level 1 appeal and I made the level 2 appeal. If this is denied as well, that is it. I cannot make the insurance pay.

I mean is this fair? Why should I be responsible for a bill due to a glitch or technical error on their end?