Just fired up Spine after 2-3 days, and it asked for the license key.
The app then downloads, loads, and as far as I can tell, starts off exactly where I left off, ie displaying the model I last worked on.
If I disable wifi, it immediately asks me for the activation code. If I then close without entering code, activate wifi, and start Spine again, it downloads, but without prompting for the activation key.
Next time it prompts me for activation code, I will try closing and just launching again, and see if that does the trick.
Update:
It asked for activation code again. Closing and launching again a couple of times did not work. I then rebooted, launched Spine, and it then downloaded and opened as normal.