Will Lego repair a bad motor?
The LEGO customer service does provide replacements for defective parts, but only for parts which are still in production. Sometimes you'll need to send the broken part back to them. They don't repair the parts as such, just replace them.

As for the micromotor, you're out of luck as it's not produced anymore. They might provide another motor as a replacement, but that's not going to help you much.

Your next option is to buy a second-hand one, for example on Bricklink (service pack or motor alone)