How to test if the USB data lines are being passed to the port?
It could be that you have a wrongly-designed dock ("port replicator", aka "USB hub") which doesn't reset downstream ports when upstream port is disconnected. Or it doesn't power off the VBUS on the ports, hubs are required to turn if off. Or it could be a badly designed RFID device. My guess is that your device (RFID) is still powered and retain old enumeration address, and therefore not responding, but it all needs debugging.

If you want to determine what is going on and who is at fault, you can probe VBUS, or you can probe D+ with DMM using the dongle you found. Probing D+ will give you an idea if the port is being reset (D+ should toggle at least once for 50-200 ms), but a DMM might be too slow for that, and an oscilloscope would be needed.

Ideally you should use a USB protocol analyzer (like this one) for the job like this, but to visualize the bus state you can use a cheaper indicator like this one.

You also can try a known good device (like USB flash drive, or keyboard) behind your dock, to determine if they will re-connect after removing and re-connecting the tablet. If they do re-enumerate, then the problem is in RFID. If they experience the same problem, the dock is at fault.