OK I had a problem like this. All my bluetooth devices (headphones, keyboard, 3 phones) would pair with windows 10 but only connect for a second if they connected at all. I spent 10 freaking hours trying to fix it and I was determined. I scoured the web and tried everything including uninstalling drivers, using compatibility mode, and about 50 other things I can't even remember (by the time I was done it was like 4 AM). Nothing worked. I finally found a post about a guy who couldn't get his windows 10 device to connect with his car. It was off topic but I was desperate. Sorry I don't have the link. Here's the deal. Uninstall all the bluetooth enumerators and devices (I didn't uninstall the radio and it didn't seem to make a difference). Turn off your internet connection. This is the important part that nobody can figure out. Uninstall you HIDs in device manager. Restart computer. Turn on internet. Re-pair devices. Worked for me - I really hope it helps so you aren't stuck like I was. It is really frustating that they released an unfinished operating system that the OEMs didn't even have a chance to make proper drivers for. Then they blame it on your computer saying it is just no compatible. I took their compatibility test. I passed and installed windows 10 and am still having tons of issues. Then they actually tried to say the compatibility test they released was faulty. They really need to get it together. Grrr.
It might be an answer that is a bit off topic but I'm guessing other people will read this thread and it might help some of them...I really hope it helps you too even though your problem is slightly different.