PEC62,
Is this a Bluetooth keyboard and mouse, or one of the Microsoft Wireless desktop combos that used the 2.4 ghz frequency, but not Bluetooth?
If it is one of the ones using the 2.4 Ghz frequency, but not Bluetooth it could be interacting with the WiFi and Bluetooth on the iPhone which also share the 2.4 ghz frequency. If it is using Bluetooth, try turning off the Bluetooth on the iPhone. It may "handshaking" with the iPhone from time to time to check and see if the iPhone will work with it. Bluetooth devices do this all the time, and it shouldn't cause them to have problems.
The 2.4 ghz frequency is used by a lot of devices includeing Bluetooth, 802.11b/g WiFi, cordless baby monitors, cordless phones, cordless doorbells, cordless security cameras, and others. It also will get interference from some electronics such as microwave ovens, air conditioners, refrigerators while actively running and electric clothes dryers.
Hope this helps,
Nathan C.