XXX:
The Rotax 912 RPM Max is around 5,800rpm with 5,500 the maximum sustainable rpm. It is certainly possible to happily still fly at 5,000 or much less, however that being said I've never experienced a drop of that many RPM with Carby heat during my several years of 912 personal ownership over 700 hours.
It was well below 5000 mate (try 4000 - 4200) on climb, then dragged itself up to 5000 on early downwind. Maybe I'd better go have another look. Drains were clear, fuel was sufficient. Electric fuel pump on. Temps and pressures normal. Left tank selected. Could not reproduce it on ground. Engine is a few hundred from needing an overhaul. Mag check OK on ground. I'm assuming it was me - the most fallible part of the system. I normally vary RPM 5000 - 4500 on downwind in the circuit to try and optimise the spacing.