You need to properly powercycle/reset the modem each and every time that you change the device that is being directly connected to it by unplugging it from the power source for about a minute.
If it is a telephony type (CDV) modem with a built in backup battery, the recessed reset button on the rear must be used rather than just unplugging it from the power outlet in order to properly power cycle it. You'll need something like a bent paper clip or a pen tip. Depress and hold in the recessed reset button on the rear until you see the front panel indicator lights begin to cycle, then release. Now give it the time it needs to re-sync with Comcast.
It's really that simple ! The modem has a MAC address cache. That, coupled with a CC residential config file, only allows one MAC addy access to the internet at a time. The modem remembers the last addy that it has seen so a powercycle / reset operation is needed to erase the memory and starts it with a clean slate to allow it to see the newly connected device.