Losing Internet Connection

[EdK]

On a 2011 IMac 10.8.5
I keep loosing my internet connection, when I open the network Preferences it indicates that the Ethernet and Wi-Fi is still connected.
When I loose the connection I can move the Ethernet cable to a Mac Book Pro and it connects to the internet OK
My Internet provider is ATT
This is the weird part:
I can get my internet connection back by removing the power and the backup battery from the ATT modem and letting it reboot

A ipad and 2 iphones are also using the same WI-FI network with no problem

Any suggestions?

 

[MacInWin]

Get a new modem from ATT. If a reboot establishes the connection again, it's most likely something in the modem.

 

[EdK]

AR&T replaced the modem and the cable to the the modem, it has been 24 hrs with no problems
Thank you for the advise