I don't think they want the BC issue to go away.
If he's shown to be ineligible, you'll have race riots in every city in the US on a scale of the race war the left has had wet dream as a path to absolute power for over 40 years.
I haven't seen anything to make me believe the left has given up on the dream of a race war as a path to absolute power, in fact everything I see indicates that's exactly what they are doing.