Eh, this isn’t accurate. You can obtain many mounts many times. Prime examples include the covenant renown mounts, mounts that drop from mobs, etc… There’s also plenty of BoE mounts you can craft/obtain over and over again for gold-making purposes. You can’t learn any mount more than once though.
As for the rings themselves, certain rings aren’t available at certain times. For example, the Stone Ring is only available when the quest “Putting a Plan Together” is up in the Necrolord Assault. The drop rate is ridiculously low as well, but people often put the ring quest up in LFG for sharing
I will agree with Moonphyre though. Once you have an account-wide mount, you’re finished in that regard. Even if the other rings aren’t showing up due to a bug, I highly, highly doubt that any effort would be put into fixing it considering it has no negative impact.
With that said, if you feel there is a bug occurring, you should report it to the Bug Report forum so the proper eyes can see it.