Hello;
That is the expected behavior for that type of counter. The DAQ STC chip (the one in the E-series DAQ devices) doesn't support trigger counter operation, only gated level operations, that is why your counter will stop counting at some points. It will only work during the high level of the gate signal.
To have the counter to be trigger by the rising edge of the gate pulse, and then keeping counting after that event, you need to work with a boad from the 660x family. Those board have a different counter chip onboard, that supports triggered operations by edge.
Regards
Filipe A.
Applications Engineer
National Instruments