First, what motherboard (or PC model) is this?
I'd definitely check to make sure you have the latest drivers, though a glance at the Edimax page suggests they haven't updated anything for Win10 in a while. You said this has been happening for a month, but it was fine before that?
When the issue occurs, is it after a cold boot or a wake from sleep / hibernation? Some devices don't do a good job waking from some/all of the sleep states, so sometimes a solution can be found by adjusting the device sleep settings in Windows "Power Options" and/or in the BIOS
If it only happens when the machine is booting cold, and given that this is a network device hanging off USB, there could well be a timing or some other issue in terms of when the whole USB device tree gets initialized vs when Windows is looking for the network during the initial boot phase. It's possible there's a BIOS setting that can help.
You will probably have to do a little troubleshooting to narrow down the problem. When Win10 is complaining about no network adapter, open an admin command prompt and have a look at devmgmt.msc to see whether the your network adapter is listed, missing, or listed with a warning (! symbol). If it seems to be there, then from the command prompt you can do an ipconfig /all to see what Windows thinks is happening with the IP stack (and, if you're in the "connected but no internet" state, an ipconfig /release followed by ipconfig /renew might fix it, or at least tell us something).