What version do you have, specifically, on what operating system? Do you have a perpetual license or Cloud Subscription?
There have been several versions that "forget" their activation status because of corruption. Adobe thinks they've fixed this with the latest updates (13.0.4 / 13.1.2).
Extended/Standard has little to do with this - there's only one software set and when it drops out of "activated" mode and returns to "trial" mode the trial always shows the Extended feature set. The root cause is that you've dropped out of "activated" mode.
The version I am runnuing is 13.1.2 x64 on a Windows 8 machine and I have a cloud subscription. Interestingly when it drops me into extended rather than the basic I have subscribed to there is no nag screen and the Help/deactivate.. menu item is accessible. (If I deactivate and rerlaunch the program I can go through the procedure to re-activate it and it then runs in basic mode till the next time.... )
If you have the cloud version, then it is supposed to be extended.
I think you may be right though when I subscribed at the beginning of the month two priced were quoted, one for basic and one for extended. Now I see that the price I am paying is the same for each and every application and gives the full version.