Verdi,
I think that the behavior you are looking for can be achieved by configuring the counter for buffered period measurement. The counter starts counting from some initial value with each rising or falling edge on the gate. You could also use buffered event counting, but the count value will not reset with each edge on the gate. I don't know what you're using to program the board, but you could start by looking at the counter examples that are installed with NI-DAQ.
Hope this helps,
Erin