I have not heard of that problem.
A1Click is probably just removing one file or entry that is causing that. All you need to do is figure out which one.
There are three ways to run A1Click. Clean PC, Remove Tracks, and Run Settings. Clean PC and Remove Tracks run a certain collection of settings. A1Click's Help tells what they are. Run Settings only runs the settings that you choose in Cleaner Settings. So if you can determine which setting is causing the problems with MM, you should be able to simply not run that setting.
The default settings in Cleaner Settings are what Clean PC runs.
The first place I would look is the User Assist section of the Registry Cleaner. If you are running that, don't. Then I would look around the MM folder to see if there might be something there that A1Click might be removing.
I hope you figure it out.