I've heard/seen this problem before. Unfortunately, I've yet to see a solid solution either.
The only thing that I can suggest, aside from buying a different brand, would be to go into any software that it came with and turn off any battery life saving features that it might have. Of course, if it doesn't have this feature, then you could just uninstall it, then just plug the mouse in and see if it picks it up as a plug and play device. Give it a go and see if that works...if it does, then you know it's the software that was causing the issue. Oh, and Microsoft recommends that you ensure that your updates are current.
You can check for drivers HERE
Not much help, and probably not what you want to hear either...sorry!
War produces veterans, wounded both physically and mentally. They have sacrificed for us.....and it is now our job to help these veterans, as they have already helped us in ways we will never know, in ways that we cannot fathom, and in ways that we take granted every day.