Recurring scheduled tasks will actually be deleted and recreated at run-time, which should be transparent to the end-user. In cases such as you have described, the task failed to re-create. If the credentials for which the task is set to 'Run-As' are invalid (e.g. the credentials fail to validate), the task will fail to re-create. Ensure that the credentials being used are valid, and are not locked or disabled.
When viewing the scheduled task, the 'User to Run As' should be a viewable field (from within the Scheduled Task Manager). If you are not being prompted for these credentials at the time the task is being created, they may be coming from the 'Default Credentials' stored within the program options ('Tools>Options'), which may need to be cleared and reset if they are no longer valid.