When I start the program, Sonar tells me that it will switch to demo mode in x days and asks me to activate. The software was already activated but I run through the offline activation procedure in any case - Export activation request and Import activation request. Once done, the same message appears telling me it will switch to demo mode. When I click on Help 'About Sonar', it shows that my copy is legal and my monthly subscription is up to date.
Any ideas?

This strikes me as a by design thing. Your SONAR is fully functional correct? The reminder is for the lapse date, at which it will revert to demo mode (if not kept current). The more important part of this is that lapsing also resets your "12 months to ownership," so the reminder is to the user's benefit.

The reminder you see is a "will shift to" and not "is in" demo mode, correct?

I had the same thing happen to me. For me it was that I paid by PayPal and had to authorize that months' payment. I switched to a credit card and the notice disappeared.

Thank you both for the advice. That is exactly the issue I have encountered.