Try disabling U-APSD support on 7260's settings and see if it still makes the router drop WiFi.
That seems to have done it. Thank you so much. The connection is no longer dropping on any of the other laptops.
Is the U-APSD support a necessary function? In other words will wireless connection be alright functionally and performance wise to just leave it disabled?
U-APSD does not affect any connection performance and stability at all. If implemented CORRECTLY, U-APSD should improve battery life while having all the speed the WiFi can get (analogous to Intel SpeedStep technology). However, some routers can't implement this feature correctly resulting to the issue you're having or sometimes speeds just slows to a crawl.
See article here: Intel® Wi-Fi Products — What are the advanced Wi-Fi adapter settings?