Well first off,
If you wanted to kill it you couldn't. If you do enough damage to it (when you have it on High Wall of Lothric) it will simply fly away leaving a Large Titanite Shard behind.
To me the same thing happened. I went through the game and by curiosity I came back and the Wyvern was gone.
I revisited in 2 points of my game. One of them I saw the Wyvern again and the other no.
- When I revisited and saw the Wyvern I was messing around in the Catacombs of Carthus
- When I revisited and didn't see any Wyvern I had just been to Lothric Castle. Killed both Wyverns there.
One thing that I'm assuming is that it can be a bug that the developers overlooked. Or it might be that one of the Wyverns at Lothric Castle is the same at High Wall. Since I killed it, the Wyvern disappeared.
Like @fhlamarche said in the comments below, he made a new character and instead of going to other areas, he went straight for the Dancer of the Boreal Valley and then to Lothric Castle (to the bridge).
There were the 2 Wyverns and when he came back to the High Wall there was no Wyvern to be seen.
Coupling the experiment with the fact that in the High Wall you can't kill the Wyvern (Like I said previously, it just flies away) it seems that the High Wall Wyvern IS one of the Lothric Castle Bridge Wyverns.
And I can't be certain because we can all speculate and later a patch
comes and puts the Wyvern back in place.
But all in all I believe it to be one of the two Wyverns at Lothric