Its a one chance deal. I really don't like having the romance/flirt dialog tied to a Charisma skill check, I think it's a bit out of place and puts first time players at a huge unknown disadvantage. Not cool.
It's not a one-chance thing. I was "best friends" with Cait and later on went back and romanced her.
Did you fail the initial romance influence check and then get another chance at it later?
Try sending them away, wait a few days and go back to them, they'll usually give you some dialogue again and the option.
I wonder if the personal quest thing was one time as well? When Nick first opened up to me, he said he wanted to share his past, I choose "I don't care" and he said fine and no more personal chats. Now I can't seem to activate the Eddie Winter quest.
I think you can only complete the dialog once.
However you can just wander off and that exits the dialog but leave the decision unmade so you can complete it later. My companions have a habit of starting these chats in the middle of the establishing or climactic cut scene of a side-quest that I'm trying to pay attention to. so I do that to them a lot.