A couple things: PD doesn't use any online resources at all, so being disconnected shouldn't make any difference to your editing performance. You'd only notice that you were offline if you tried to download content from Shutterstock, for example.

I have PD365 installed on two computers and I just tried opening it on each of them with no internet connection. I'd used PD on each one within the past week and neither one prompted me to connect.

That's different behavior than when they're both connected to the internet, as I always get an activation notice on the my laptop if I try to run PD365 on it because CL has to transfer the "active" license from my main desktop machine. I'll then get the same messsage on my desktop when I want to use the app there, but I've never been prompted like how you're describing.

You may want to open a support request directly with CL here.