Pete;
I agree that is a little strange.We don't have such problem reported on our Data Bases.
A workaround you can try is to make a sinle pulse goes to the source, before start the buffered acquisition, and see if that makes the counter keeps reporting a 1 value.
You can also try the same thing on another counter of the board to see if that problem is related to the counter you are using.
Regards
Filipe A.
Applications Engineer
National Instruments