Try using WD40.......... Spray a little onto a cloth and then rub it onto the mirror. Make sure the mirror is clean first.
Do not get the WD40 behind the mirror.....it will dissolve the adhesives that hold the mirror to the frame.
This works Guys.....
Try using just about any Method brand surface cleaner. They have bathroom wipes, sprays, multi-surface cleaners, etc. A couple sprays and a wipe every few weeks and you're all set.