The A380 route network that BA is currently flying is MIA,SFO,LAX,SIN,IAD,DFW,JNB and BOS. I believe 10 of the A380 planes are currently operational. The out of action ones being G-XLEJ in Manila on an extended heavy check and G-XLEL which appears to be stuck at LHR since 21st August.
In essence the route network they fly is too onerous for the fleet size they have and when you couple this with the fact that BA stored their A380 fleet in less than optimal conditions plus there is a shortage of A380 pilots in BA then when the inevitable happens e.g. tech problems, slot delays,LHR delays etc then the impact cascades through the schedule and BA are forced to endure heavy delays or cancel flights. BA likes to sweat their assets as much as possible and they do this for their whole fleet - short haul and long haul. I don't have any figures for airframe utilisation but my suspicion and ad hoc research seems to suggest that BA (and I assume IAG) utilise their planes more than their peers.