You may have encountered a known issue with notifications: when the submitter's email address is not a valid email address, notifications are not sent.
Under Options -> Email Notifications, please check that the From address selected in the drop-down is either "FormsCentral Notifications" or a field where you would expect people to enter an email address. If that is not the case -- for example, if the field for the submitter's first name is selected -- that would explain the problems that you are seeing. Otherwise, please verify that the individual submissions under View Responses contain valid email addresses for that field.
If you have missed notifications for submissions with valid email addresses, please share the form with either me or Brian and we'll try to uncover what the problem is. My apologies for any inconvenience this may have caused you.
Thanks Eylon and Brian. The "submitter's first name is selected" was the problem.
The bug needs fixing obviously. I spent too much time trusting the process and assuming I was at fault.
I really appreciate the quick and precise response though! Thanks.
Time now the programmers to sort it out!
Please see my note to Eylon.