Hmmm, forgot to mention my theory, didn't I? About the continuing relationship...
My thought is, and don't hate me for this--if you get angry and explode at Solas when he leaves, it's over for good, even if there might be content about the romance later on available to others. You did what he wanted you to do--you got angry and let him go, and it's so much easier to leave you if you're angry. (Could be this is why some people say there's a bug and they can't ask him "about us?") That said Lavellan has every right to be angry. The breakup was completely unexpected, given the context.
If you say, on the other hand, "I believe in us," or "I love you," (or other non-angry options) there's hope for a future with Solas. But there's the possibility, as I pointed out, that it won't be a happy one, unless Lavellan can be immortal with him. If she cannot, then he has to watch in agony as she ages and dies, like humans in his time. To him, it would be like she's slipping away from him more the harder he tries to hold on. And you can bet he'd be trying to hold on. She's his Anchor in more ways than one by the end of the game. She is his primary connection to the modern world.
Why do I think anger ends it? ... Well because in getting angry you're saying you understand that it's over. You're not saying you think things can be worked out, or telling him that you love him and he shouldn't leave you like this. Basically you're accepting that he's just ending it right there, and understandably you're peeved about that.
And also because Solas is completely a sucker for Lavellan and hates the thought that he might be hurting her... so I think he might be more willing to patch things up if he thinks he's caused her deep pain by leaving, or if he eventually misses her and remembers that she said she thought it could work out etc.
Again, don't hate me for this - it's a theory for a reason. After all, the romance only officially counts in that final scene where he leaves you (and that is so unfair, and to go on a tangent, I'm completely tired of romances for women being the ones who run away/cheat/go on about past significant others/die, and NO, Cullen is not proper compensation when we also got Blackwall who ends up being more than a little sleazy... and guys seem to normally get romances who are pretty steady and reliable and don't die, run away, cheat, or go on at length about their past loves making them feel as if they are second best to, for instance, a dead wife...).
... And yeah because of that tangent I went off on? That's the primary reason that I hope there is more content for Solas and that it allows for us to somehow end up with a happy ending for him and Lavellan. If not... then I will have to add him to my list of reasons why going for one of the romance options for straight females in a BioWare game generally doesn't end well.