Skyhold - why abandon it?

That does bring up the question as to what will be done with it if the Inquisition is disbanded. After all that work restoring it, seems a shame that the Inquisitor no longer has much say as to who does what to it.
The thought of a noble using it as their fourth seasonal home...*shudder*

I'm not sure if the Inquisitor would abandon Skyhold, even if the Inquisition is disbanded or now serves the Chantry. Morrigan says something about the previous owners of Skyhold not knowing what they had and that you would appreciate it more (or something like that). In Trespasser Solas reminds you that: "You have a castle, an army and a title that leaves every world leader quaking in fear. Be content." This makes me think they intend the Inquisitor to keep Skyhold, but on the other hand Solas said that before knowing that the Inquisition was disbanded/or now serves the Chantry. Who knows... of course if the Inquisition was disbanded to avoid Solas' spies, then it would seem like staying in Skyhold would not be the wisest thing to do... since it's a place he knows more than well. And if they're really going to Tevinter then it would seem like Skyhold will be left behind... maybe it will be abandoned again, difficult to say.

Skyhold is in a pretty bad place for a headquarters really. Its too far from everywhere, and while it is defensible it seems like it would also be relatively easy for a small force to trap you in it.

The other thing for the Inquisition not staying in Skyhold is the eluvian placed in one of the abandoned rooms. Since Solas has control of all of the eluvians, he and his agents can easily infiltrate the fortress. Plus Solas knows the place better than anyone like others have said.

^ If Morrigan did take the eluvian with her, Solas will override it to take control. That guy is a manipulative bastard.

I'm all for a batcave like headquarters if my ex Inquisitor can't stay in Skyhold.

Skyhold belongs to my Inky. Its a place they can retreat to get away from it all.

While you had all the financial resources available to the Inquisition to ensure supply lines, then staying in Skyhold seemed viable. Once you are reduced in size it is far too remote to be practicable. A peace keeping force needs to be closer to the areas it needs to police and likely to be attached to the Cathedral in Val Royeaux, since you are meant to be working directly for the Divine and Ferelden made it clear they no longer wanted you on their patch. If the organisation is disbanded then what use would the PC have for a castle in such a remote location? Better to go to Kirkwall where Varric has arranged for a title and estate and is more centrally placed. It may not be the most fun place in the world but it is a good jumping off point with trade links to many places. Skyhold will probably continue to be used as a place of pilgrimage for a few years at least. It would be okay for a retreat for a few weeks rest but not as an HQ if you still intend getting involved in world affairs.

I always thought of Solas as your kind-of Merlin (before the big epilogue reveal).