You have eliminated the cable as the source of the problem.
And if the portable drive is connecting and working on other computers then the portable drive is okay.
That leaves your PC as the culprit.
Did you try running the Windows 10 troubleshooters?
And, although somewhat more involved, you can reinstall the USB controller drivers via Device Manager.
Sort of narrowing down to either a software/driver problem or perhaps a hardware/motherboard problem.
Another tool that you can use is Event Viewer. That is more involved but the Event Viewer logs may be capturing some error code or warning that takes place just before or at the time of the connection failure(s) and the "bingly-bong".
Here is a link from within this forum to introduce you to Event Viewer:
http://www.tomshardware.com/faq/id-3128616/windows-event-viewer.html
Suggest that you take a look at the link, and then the logs to see what the logs may be capturing.
Just explore the logs at first and get a sense of the organization and the data the logs contain. Do be aware that some logs will say they are empty but what is really happening is that data is being gathered up for presentation.
And also be aware that right-clicking any given log entry will provide additional information.
No need to immediately react or do anything beyond the logs at this time.
The goal is to find the problem. Doing so can and does take time and effort.