Cannot get multiple wired connections with Comcast
I have a (2013) Airport Extreme base station. I am on Comcast Xfinity using a Zoom modem that I purchased. It is on the approved list of modems from Comcast. With the Airport I can only do wireless connections to get on the internet. They all work great. Every wired connection - even a single one - plugged into the Airport will stop working after about 24 hours. I know that the cable modem only assigns a single IP address. But I thought the Airport was supposed to be able to manage multiple wired connections into it, just like it does with wireless. I have 2 devices that are wired and I am unable to use them.
This has been a problem since I bought the Airport. I talked with Apple tech support and they said my modem must be configured wrong. But when I open up the Admin page for the modem there are no options to adjust or configure anything.
Do the wired connections on the Airport work different from the wireless? At my last home I had an older Airport connected to a cable modem and it easily handled multiple wired connections. Is there a setting I need to make in the Airport Extreme? Or do you think I really have a bad modem? Do I need to install another router or switch or something in between my modem and the Airport?
iMac (27-inch Mid 2011), Mac OS X (10.7.4)