Thank you for the suggestion. This is the response I got from the manufacturer in case it will help anyone in the future.
"Unfortunately you are seeing the limitation of the counter of the E-1608. It has no gate and is time controlled by DASYLab’s timer which is subject to the operating system’s hierarchy of priorities. Meaning, other parts of the Windows operating system will periodically be given a higher priority than DASYLab, and so there is an occasional lag in the counter read. This is true of DASYLab or any program attempting to read that counter."
So it looks like I'll need to go with a PLC.