Humm, I would contact their customer service after uninstalling it and then reinstalling it- if it still doesn't work then a part of your registration may have not have been right.
The standard: Have you tried turning it off and on again? Rebooting your computer, uninstalling and reinstalling? Licensing issues shouldn't cause this, as the trial has full save functionality and when your trial is expired SAI just won't open.
If you got the free trial version from their website, it expires after 30 days and after that time is up, it won't let you save. The option will be greyed out and you'll get a little red message saying that your trial expired or something similar.
Link
Patromeris
Try exporting the file?