Special personnel casualties - timing of effects

We came across a novel situation yesterday, where an Elite unit moved 2 hexes and battled. The defending unit used Ambush Combat card, and as a result of the hits taken by the attcking unit, a die roll was made for the Special personnel figure, and it was lost. This made the remaining unit NOT Elite.

We resolved this according to the Combat card, which stated that the unit battled as planned if it didn't retreat or be eliminated.

However, it got me wondering about other timing issues of this situation. e.g. Bombers, LMGs and Flame thrower SP. I would guess that their loss has immediate effect in such situations.
Is there any ruling on this? Simple sequence of events?

Mark, It seems that the beneficiary effect of having the SPF would be lost after the AMBUSH is played if the SPF is removed because of a "Skull" roll.
This makes sense to me as maybe the momentum of that persons loss diminished the battle readiness of the remaining troops.
"War is hell"

I play a lot of Memoir '44 (another C & C game). This situation comes up when a full strength Japanese Infantry unit [4 figures] is ambushed. Normally that unit would get 4 dice to attack, but if ambushed and it loses one or more figures it now only attacks with 3 dice.