NetGear Router dropping connections seemingly at random

I am currently having a problem with my router where the Cox DNS server I am connected to stops resolving host names. Then both Wifi and Ethernet connections will disconnect from the gateway and reconnect shortly afterward. 

What can I do to remedy this? It used to happen months ago but stopped mostly when a certain member of the family moved out. They recently moved back in (leading me to suspect them). They only use a single mobile device to connect to the router so it seems highly unlikely that it is causing such a serious problem. That could be chalked up to coincidence I suppose.