Wireless Keyboard/mouse Problem.

About a week ago I ordered a wireless mouse and keyboard for my computer. I got the mouse first and the keyboard a few days later, so I had been using the mouse for a few days and it was working just fine. I finally got around to installing the keyboard as well and within minutes started having trouble with the mouse.

It will randomly just stop working for a few seconds every now and then and out of habit I pick it up and shake it (which is kinda weird because that is a ball-mouse habit and I haven't used one of those in like 3 years). On top of that it will randomly get little speed boosts or slow down when moving. Now and then it will even not register clicks.

While all of these new features make playing Diablo 3 much more... exciting... I would rather do away with the problem.

The mouse I have is a Logitech M510.
The keyboard is a Logitech K800.

Some things I have tried so far...

Used Logitech's special software to pair them both to the same receiver.
Tried having them on different receivers in various USB ports, including having one in the back and one in the front.
Used them both separately and each works fine alone.
Uninstalled and reinstalled them in either order.

If I move them about 4-5 feet apart (the keyboard and mouse) they work with no problems, but then the problem is that they are 4-5 feet apart.

Anyone have any experience with using 2 wireless input devices and/or having similar problems? Any troubleshooting tips would be appreciated. All I found online was pretty much check the batteries and make sure you aren't sitting on top of your router.