So after years of frustration with this nasty problem, I've finally found an answer to this problem. It seems that the reason that the admin credentials request appears is because, by default, MM tries to reset file associations which it can only do if you log on to MM using admin credentials. This really is something that the MM devs need to fix. Please do not make the setting to reset file associations the default setting. Mere mortals are not going to figure this out by themselves (it took me, an IT pro years to figure it out) and so what people will do is let their kids run as admins on the system to work around this problem. Therefore, MM forces users to be less secure. This is unacceptable. Please fix the default setting.
To fix the problem:
Tools -> Options -> under "General", click OS integration -> clear the "Re-associate File Types on startup (recommended)" check box.
Get answers about using the current release of MediaMonkey for Windows.