Range Extender losing connection

I have a combo wifi modem from Cox.  We've been having trouble with wifi signal strength issues in parts of our house, so I picked up a range extender.  Connecting the extender to the wifi was no problem, everything paired great and I was able to get devices connected from the other side of the house that used to have trouble staying connected due to a weak signal.  However, the day after installing the extender, it started losing connection to the wifi modem.  The signal strength (from the extender perspective) would still be fine, but the modem kept seeming to kick if off.  Within 10 - 15 minutes, everything would be fine again.  Few hours later, the extender gets dropped again.  Thinking it might be a faulty extender, I exchanged it for a new one with the same results.

In general our combo modem has always seemed a little twitchy, having to be restarted once every few days.  The ethernet connected devices would be fine, but nothing could connect to the wifi until a restart.  That has settled down to only needing restarts every week or two, but the extender issue happens multiple times a day.

Do the Cox combo modems not allow for 3rd party extenders to be used?  Is it possible I need a new cable modem?