Departing Runway 7L on the ANCHORAGE FOUR SID from ANC; the pilot of a C525 experienced loss of NAV data on the FMS NAV display.

Narrative

At start of taxi we were assigned Runway 32; but requested Runway 7L. Entering Runway 7L into the FMS produced no ANC4 departure for the runway in the Collins 3000 FMS. We notified the Controller that we did not have a coded ANC4 for Runway 7L and were informed that ANC4 was a valid departure for Runway 7L. We then entered the ANC4 into the FMS; and it did come up so we keyed our VNAV and NAV functions for the autopilot and accepted the takeoff clearance. Upon liftoff; the departure disappeared from the PFD and the FMS. Then we manually brought up the chart and; when noticing the turn to 200 degrees; started the turn as the Controller gave us a vector turn as well. Collins in ICT was called and a return call; confirmed that because of the type of departure -- 3 different patterns for Runway 7L -- the departure would come up; but then disappear because the Collins database is incapable of separating the 3 different flight paths. Lesson learned is that we should not have accepted the takeoff until we reviewed the departure completely and in the future we now know that this anomaly may occur again and to review every departure procedure completely.