I keep having romances, but after awhile they break it off. Can you start going out with them again after awhile? Anything special you should do? 
If they haven’t disappeared from your screen, it is in fact possible to salvage the romance, or at least a friendship. You will need, however, to spend several days socializing with the person one-on-one with events they enjoy and build up again. I don’t know if they ask again to go out with you, but I would think that they would.
If your romance is still on, but waning, and you aren’t having a whole lot of time at the moment to socialize (romantic dinners, romantic movies are the best for a girl/boyfriend), you can purchase a gift (the wrapped box) and they will, in my experience, respond happily to your thoughtfulness.
The main ‘trick’ to keeping a romance going is to see them a lot.