In my view, dance romances are similar to office romances. A total non-issue for some, but for others a huge issue.
The problem is that, like offices, dance communities tend to be small, gossipy and closely interconnected. So what happens if/when the romance ends becomes a major issue for some people. Also, even if the relationship is just fine, there will be ups and downs. Observers can't help but see what's going on and speculate.
People are pretty gossipy creatures, I think. And having people gossip about me doesn't bother me much. But knowing that people are talking about you compounds the pain of any breakup. I hope that makes sense.
I'll give a couple examples.
When I had my little crush on my friend/dance partner, I had more than a few people ask me about it, subtly, or make references to my relationship with him. I brushed off the sideways requests for info, and lightly told people we were "very good friends," which was true, then and now. But people were curious.
When a local dance couple broke off their partnership/relationship last year, there was all sorts of speculation behind their backs about a romance gone sour.
When a gentleman at my former studio was going through a rocky patch in his marriage, everyone speculated behind his back about potential outcomes. When he divorced six months later, ladies literally fought for the poor guy's attention, and it got really ugly, until one lady "won" him for herself.
So I guess my answer is that it's not different from any other romance, but because of the fishbowl effect, any ramifications are magnified. If you break up from the girl you met by chance on the train, you never have to see her again. But if you break up from your dance partner, chances are you'll see her again, lots of times.