TRACON Controller providing OJT described a failure to complete Tower notification requirements during CENRAP operations; complicated by split sectors to enhance training familiarization.

Narrative

I was conducting OJT for a developmental on RADAR. The Supervisor suggested splitting the RADAR (West and East) for training due to an abundance of staffing. This in itself was fine; moderate traffic at the time and splitting is a good training tool. After the split occurred; and the Trainee was getting his bearings on how to work a split final; the RADAR went out; and we had to go to CENRAP. With our procedures on working inbounds during a split operation; we have to get a sequence number for our next arrival from the person owning final (in this case RADAR West.) Being that we do not have the staffing to work a split operation very often; to say that our abilities are rusty is an understatement. During CENRAP; RADAR is required to call inbounds to the Tower; and that did not get done while the RADAR was out. With the moderate traffic; complexity of splitting the operation; and then dealing with a runway change (which means map change; frequency changes; approach changes and trying to talk through all the procedures with a trainee) calling inbounds to Tower simply slipped my mind. I do not think that the RADAR West Controller nor the Supervisor who was monitoring the operation during the outage caught that [the] inbounds were not called either. More staff so that we would be more proficient in working a split operation. A RADAR update that works the first time; without having numerous outages after the installation.