I did a troubleshooting testing in various power plans; balanced, high performance, and Power Saver.

High Performance power plan has "selective suspend" disabled while plugged in, I experience the same issue while in this configuration.

this is completely inline with what I'm seeing.

Additionally, I thought the issue might be related to the new screen scaling capabilities in windows 8.1 so I tried the "Let me choose one scaling level for all my displays" option in hopes to remove that.
This did not help.

It sounds very much like there was something new introduced in Windows 8.1 that's not playing nicely with the earlier driver - maybe in the way memory is managed or something.

EDIT: James at DisplayLink suggested trying a USB hub, which has given me some limited success. Not a long term solution, but worth a try.

I got mine resolved, it's power too low, use USB Y cable to boost power.
 

I have the same problem, windows 10, toshiba AMD A8 4500, USB 3.0 is using AMD USB 3.0 eXtensible Host Controller 0.96 by Microsoft. Turned off all power management still didn't work. My USB 2.0 works though, so that means displaylink driver is installed fine.

Amazon reviews that are mostly positive but those are mostly mac users, but why it works for them? Probably because USB-C supplies 1.5A to 3.0A. So as suggested by displaylink support suggested to use Y cable. Ordered an external USB hub with power supply, plus a Y USB 3.0 with 2 male to 1 female cable. Plug the 2 into the hub, plug the displaylink 3.0 to the female and low and behold, works !!!!

so check your device USB 3.0 controller Event, if you see device migrated, device installed, device not started, it could be that it just doesn't have enough power when a certain rendering is needed, so it went off, came back on and windows thinks it is plugged in and detected a "migration" and installed again, then it's likely not enough power supply on the USB 3.0 port.