With the Fluke set to DC reading it has a imput impedans of around 10MOhm
Do you have another meter so that you could measure the voltage
simultaneous with the faulty fluke?
Just to make sure the fluke isn't affecting the source in anyway?
If only dc voltage is affected (and dc current is fine?) it might be as simple as a bad
contact on the range switch.
btw, How did you conclude ac voltage is fine, just stuck it an outlet?