According to the Release Notes, driver revision 126.96.36.199 applies only to Renesas uPD720201 and uPD720202 chips. If you use driver revision 188.8.131.52, it means your chip is another model.
I had similar problem with my Seagate GoFlex external USB 3.0 drive. I have solved the issue with upgrading firmware of the drive, not USB card. I would recommend to do the following steps in your case:
Try to attach your docking station to USB 2.0 connector (if it is possible). If the issue is resolved, at least you will have a reason to address the issue to Plugable.
Try to find similar problem description in community forum section of your disk manufacturer or try to ask this question at that forum. May be you find a clue to your problem. Commonly power management issues are pretty complex and commonly it is not clear, which part of hardware/software contributes the most to the problem. It might be computer itself or its bios or software settings, or the card driver and its settings or the disk itself.