That was how I read your first sentence. I was like, "KILL HIM! KILL HIM WITH FIRE!"
On-topic: Well, considering Maya was probably the most sane/innocent out of all the adult characters in the movie, I think its safe for her to be bad at her job, if she is. Its not like she is consistently bickering, half-assing her job, and directly defying orders from her superior, like the average person who gets fired would. And anyways, I think you would have a hard time hiring people into a company/organization/etc. that puts so much stress on the human mind, let alone know that if you screw up the entire world will perish. I think Nerv will need all the hands it can get, let alone want to fire them. The only reason why Gendo let go of Shinji so easily was because he knew he would come back. Ritsuko got fired because she destroyed the things she created, which was basically the secret sauce of Nerv.