Some quick thoughts.
Check notification method against the user you are trying to email in the reminder and see if set to "External"?
If you are sending the reminder based on "Supplier" or "Customer" then check the users in that group have "receive group messages" (ie do "Modify USer Group" for user in users node under the relevant group in Administration")
Assume the raise user has a valid email address in their profile.
When you say it does sucessfully generate emails, do you mean that the reminder shows in the tree or other users are successfully copied Ok for that email; just not the raise user?
Is your "is active" check box on the reminder window checked or unchecked?