New KM714 keyboard & mouse problems

I just bought a new Optiplex 3020 and purchased the KM714 wireless keyboard and mouse. Within a week, the mouse started ... hesitating, I guess you'd say.  It wouldn't respond to being moved, or responded very late and unreliably.  Changing the batteries didn't stop the problem. Moving the dongle from the back of the computer to the front (nearer) didn't help.   I raised my computer off the floor so the dongle is nearly at desktop height, about a foot closer, but that didn't solve the problem.  (The keyboard and mouse are less than 3' from the dongle.)  Picking up my mouse and using it about a foot away from the dongle DOES help, but I'm right-handed and the computer is on the left, so that's not helpful to me other than as a very short-term, temporary fix. There are no other wireless keyboards or mice in the room that might be interfering.  I moved my cellphone from its usual spot on the desk so it's not in the line between the dongle and keyboard/mouse and that didn't appear to fix it, either.

Shortly after the mouse got lazy, the keyboard started doing its version of the same thing.  I'll be typing along and suddenly the keystrokes stop appearing onscreen.  If I don't notice immediately, then whatever I've continued typing gets garbled, when (or if) it does show up, in whatever place I may have clicked in the meantime.

Am I supposed to manually turn off the keyboard and mouse at the end of the day, or when I step away from the computer for any period of time? 

Any other advice?  I love the size of the new keyboard but this problem is seriously interfering with my productivity ... which is why I bought the new computer in the first place!