Can a Quit Claim Deed be rejected?

Yes. A county recorder can reject the filing of a quit claim deed. It may be rejected if it is not in proper form, not notarized, or for other defects in the form or legibility of the quit claim deed. For instance, if the notary stamp is not legible, the deed could be rejected. This is one reason it may be best to record important documents personally. You did not ask, and I am not making any attempt to answer, what effect the recording may have, what credit reporting the association may make despite your recording, etc.

Deeds are recorded with the county recorder. The recorder's office will not reject a deed in proper form. I'm not sure if this addresses your concern, but there is no one else who could "reject" the signing or recording of a deed. If there is no lender involved, even years of homeowner's dues might be small compared to the value of the property. You should consult with a real estate attorney as soon as possible.

Better hurry and get the deed recorded with your land records division. Make sure the quit claim deed conforms with California law. Bankruptcy court could undo the property transfer, but you did not mention a bankruptcy. Consult with a real property attorney ASAP. Time is of the essence.