Finally solved this, it appears some messages got placed on the phone message system instead of being on Cox, so the phone showed messages, but they weren't available when I called Cox voicemail. All other messages were always on the Cox voicemail, as one would expect. Not sure how they got to the phone, but I was able to erase them.
Kansas...was looking at some older forum issues. I'm guessing that your messages got rolled over to your phone answering machine because COX was recording a message at that time. Since you are primary on the Cox Voice, a busy signal where you were either talking or a message was being left, caused to roll over to your phones answering service. Mine is set up just the opposite, so I get an occasional Cox Voice mail and don't know till I check the Web Voice Tools.
Kansas...I previously posted a link on Voice mail..however, it may not address your issue.
Is your showing of the 2 new messages appearing on the Phones answering machine window, but you are getting No actual messages left when you try a phone playback?
Login to the Cox online Phone Voice Tools and see if the Voice Mail there was activated. If you see entries here, then maybe the Cox Setting/pickup is set lower than the actual Phones Voice Mail/Answering. It took me a bit to wade thru this 2 Voice mail storage locations.... You can also check the Call History to try and pin down when calls are received and pair them with when you think messages are left. Do testing with your cell phone calling and leaving a message.
You can also check the Phones CallerID history, looking to sync up the calling times. I'm not sure by your post what is actually missing....looks like the indicator on the physical phone answering machine is incorrect and not getting updated. Maybe pulling the phone plug may work.
Kansas...I had wondered it this ever got resolved. Your situation was different than mine cause you use the Cox voice mail as primary. If the pickup ring time was less than that set on the phone's answering machine, I would expect Cox Phone history would show the voice mail...however, I would not think the phones voice indicator to post the call message left on Cox mail.
So, if the phone message pickup is greater than the Cox voice pickup rings, you should never have any indicator or actual message on the phones voice. You could check the Cox call history for the times when messages of stored (120 days), looking for any conflict where 2 voice messages are left, one on each recorder. In my case, I was talking on the phone so my phone answer machine could not pick up, so the caller got transferred to the Cox voice mail. The call history may be something you could investigate next time.
When Cox voice mail is primary, is there any indicator that a message was left...like an App or maybe a blinking lite indicator on the phone. Curious about your exact situation.