Same issue here...
Just recently subscribed to Office 365 Medium Business with 12 users. All users except for one has no problems. This one users Office keeps asking for License Activation no matter what office program he opens. When the activation pop-up is cancelled, it does appear that the program isn't limited and everything works as normal.
I've deactivated the install in my Office 365 Account Hub and completely removed the software. I then re-install, but still the License pop-up appears. I've even gone as far as to completely format the machine, but the pop-up still appears.
The pop-up is annoying and I find it very disappointing that there is no fix for this.