You can do it until you run out of time. If you’re talking about someone who dances professionally, there is no time for martial arts. That’s their life. When you’re putting in a 16 hour work day on your physically demanding job, you’re not going to pop out and go for more exertion… well, most people won’t anyway.
Dancers that have free time do sometimes practice recreational martial arts. I mean, it’s one way to work off stress. Some forms like Tai Chi can be fantastic relaxation. But, unless they give up dancing, and commit their life to their martial art, they’ll never be masters.
They probably won’t even be particularly good, but so long as they’re paying their dues, putting forward legitimate effort, and showing some improvement, their instructors will probably be happy. The critical part is paying the dues. Remember: your dancer’s hobby is their job.
But, you will never achieve martial arts mastery by day tripping. It’s not something that you get for putting in an hour a week for twenty or thirty years.
It’s a time commitment as extensive and strenuous as their day job. You can be a professional dancer… or a professional martial artist. You can’t be both. There aren’t enough hours in the day. And, since I didn’t say it, but probably need to anyway, you can’t be an “amateur master” of anything. Actually mastering
something anything requires a serious commitment.
Also, when I’m talking about training interfering, what I tend to glaze over is, this is something your character will be subconsciously choosing for themselves.
If one of these things is making them money, the other is costing them money, and they’re basically happy with their life, the priority will be obvious. If they’re not happy with their job, then that will show, and they’ll be looking for new employment; based on what I know of how competitive professional dance is as a career path.
Finally, training atrophies. Martial arts, and dancing, aren’t like riding a bike. If you don’t use it, you do lose it. Not all of it, not the information, but the ability to actually perform? Yes, that stuff needs to be maintained or it will slip. Just because your dancer was a martial artist as a kid doesn’t mean they can still perform as an adult. If they haven’t been using it, they won’t be able to keep pace with someone who has had more recent training, to say nothing of more training. In a real fight, without maintaining their skills, they’re going to have a hard time dealing with untrained opponents.