The limitation doesnt seem to involve communication with Adobe servers; its appears to be based solely on the machine time. I suspect that the Flash player on OPs machine has been connected to the internet and updated Flash Player at least once in the last 3 years.
Indeed, the laptop has been disconnected for days. I (or, more precisely, Windows) inadvertently updated to a more recent Flash version containing the "time bomb", so now the application simply checks the system date and decides whether to block it or not.
If I could "sandbox the clock" for this specific application, that might work, but I don't think that it is possible.
Genius! Good to know it exists, if I need it one day.
For now, I tried patching the timestamp in the binary as suggested by jtvjan, since I saw it before your post. It works, so I'll stick with it for now. But I'll be sure to try this RunAsDate when I need something similar in the future.