Yes. The readme file that comes with ActiveSync states that the USB connection is not stable through a USB hub. A port replicator is just a fancy USB hub. I have the same issue as well. My work-around is to use my cradle only for charging and then connect with ActiveSync via Bluetooth.
I use a Targus Mobile Port Station and it works great. Have used it for about a year now. Since the Axim has it's own power, I think it should work even with unpowered USB hubs.
Another thought...not only using a USB connection through my port replicator is flaky, it is also SLOW. With my setup, there is a noticeable speed difference using BT with AS vs. USB.