Here is what I did to fix this problem (no, I don’t know why it works, but it did for me):
Step 1: Click on the up arrow on the taskbar to reveal the “customize” link in the pop-up window. I did NOT unlock the tasbar as some have suggested.
Step 2: Click on the “customize” tab and make your changes to “show icons and notifications” for those icons you want to have appear permanently in the taskbar.
Step 3: Log off your profile. Do not restart, just log off.
Step 4: Log on to a different user and make the same changes as in Steps 1 and 2. I did this to see whether I had a corrupted user profile and to see whether it would work for another user.
Step 5: Log back on to your user profile to see whether the taskbar was properly saved. The icons appeared this time!
Step 6: Restart your computer and log back on your user profile to confirm that the icons still appear. This time they did!! For some reason, if you make the changes to the taskbar and restart your computer, the user profile information was not saved. However, if you log off, they do. I don’t know why this worked, but it did for me. Good luck.