If Fort Dawnguard, Castle Volkihar, etc. exist, then the DLC is still installed.
Your question implies that you visited Dayspring Canyon and verified that Fort Dawnguard is still there. If that is not the case, and the fort (or the entire entrance to Dayspring Canyon) is actually gone, then you should reinstall the game and load your last save from before the DLC disappeared (do not attempt to load a save you made while the game was broken).
The Elder Scroll itself is from the base game, and not the DLC. Thus, it will not vanish if the DLC gets uninstalled. The DLC does, however, rename it to "Elder Scroll (Dragon)," so you can look at the name in your inventory to see whether that rename is still in effect. If it's just called "Elder Scroll," then the DLC is most likely gone.
If the Fort is still there and the Elder Scroll is still labeled "(Dragon)," you do not have a "vanishing DLC" problem but a "quest fails to progress" problem. The broken quest is probably one of the following quests:
- Seeking Disclosure and/or Scroll Scouting seem to best fit your symptoms, but these quests are very simple and I can't seriously imagine either one breaking in the manner you describe.
- Discerning the Transmundane is much more complicated, and I could imagine it breaking, but I'm not really convinced that this would cause problems for you if you have actually obtained the Elder Scroll from it.
- Chasing Echoes is for the other Scroll. I don't think it's relevant to this.
- You should have already completed Prophet, so that probably isn't relevant either.
Each quest has a bugs section which you should consult. Unfortunately, the easiest way to fix problems in Skyrim is to use the developer console, which is only accessible on the PC version of the game, and so you might not be able to find a workable fix here. You might have to reload an older save.