Make sure that the triggering controls on the counter are set appropriately for the signal coming from the GPSDO.
Typically, the output of the GPSDO will be CMOS levels, i.e. ~5V and ~0V. Check this on a scope. Also make sure that the rise and fall times are nice and clean. Then set the counter for DC triggering at a voltage of ~ 2V5. Use 50 ohm coupling if the GPSDO allows it.
If you notice that the reading is always up and down over a tight range you might have external noise messing with the counter. I usually use a low pass filter to remove interference from local high-power FM stations.