It's a known issue on the Swype beta forums, after rebooting the phone some users have to change input method to another keyboard and then back to Swype. Next time I'm on there I'll check to see if there's any update on it.
Edit: If this is the same problem that you're experiencing, it's still listed as a known bug:
Swyping produces a blue border, error sound, and no text, immediately after rebooting
The phone is trying to load the Swype application before the ESN system variable has been populated. When Swype tries to load the license, it cannot match the ESN, and fails. Reloading the app by long-pressing a text input box, choosing "Input Method" and selecting Swype will resolve this issue for you until your next reboot.
NB. When this first happened to me, I didn't realise that my phone had been rebooting, but a quick check (Settings, About Phone, Battery, Up Time) showed that the phone was rebooting once or twice a day, which turned out to be a kernel issue.
Hope this might help someone.