How can I access a Bitlocker protected USB drive more than once on any of my PCs? This used to work (of course!)...

Question

I accessed a Bitlocker protected USB memory stick on Saturday on my PC (Win 8.1) for the first time after a year or so.
I entered the unlock password and was presented with the list of files in Explorer. After working with some of the files, I ejected the USB memory stick and removed it from the PC.
When I connected the USB memory stick again this morning to my PC (still Win 8.1), the USB memory stick was not recognized any more. There is no prompt to enter the Bitlocker password and when I double-click on the drive icon in explorer, I get the message "Please insert a disk into Removable Disk (X:).
Fortunately, we have more than on PC in the family...
I connected the USB memory stick to another PC (Win 10 Home). No prompt. When I double-click on the drive icon in explorer, I get the message "Please insert a disk into Removable Disk (X:).
Then, I connected the USB memory stick to a third PC (Win 10 Pro). I first got a message along the lines of "Access to drive denied", then the Bitlocker prompt for the password. After entering the password, I was again presented with the list of files in Explorer. I ejected the USB memory stick and removed it from the PC. When I connect the USB memory stick again it is not recognized any more. There is no prompt to enter the Bitlocker password and when I double-click on the drive icon in explorer, I get the message "Please insert a disk into Removable Disk (X:).
I tried the same procedure again on the last PC in our household (also Win 10 Pro). I connected the USB memory stick, got a message along the lines of "Access to drive denied", then the Bitlocker prompt for the password. After entering the password, I was again presented with the list of files in Explorer. This time I copied the contents off the USB memory stick before ejecting and removing it. When I connect the USB memory stick again it is not recognized any more. There is no prompt to enter the Bitlocker password and when I double-click on the drive icon in explorer, I get the message "Please insert a disk into Removable Disk (X:).
I would appreciate if somebody out there has a solution other than finding a different PC each time I want to access this Bitlocker protected USB memory stick. I copied of course all the files off the memory stick but I am curious now.
I went up and down the Internet, browsed through dozens of "5 to 7 best solutions for USB disk not accessible" from DISKPART to black magic, and tried many of the magic incantations suggested.
Thanks for a solution. The fact that I can access the drive once per PC indicates to me there is something going on in Windows.
Many thanks
Peter