Creating a new database does not carry over appointment reminder rules. For a ClinicOffice rule to run, you will need to be logged on at some point during the day to that database.
It could also be that you have run out of credits. This can be checked from the SMS setup screen, under the VIEW tab, then Program Settings menu.
If you feel that have have checked the above, and reminders still aren't being sent, then please let us know so that we can assist further.