It depends on the context (by the way, you should always include at least one example sentence in your questions, that way you can get more focussed answers)
1. "Hurry up! We're missing the movie!"
2. "I really miss my hometown"
3. "I'm really missing my hometown"
1. is perfectly correct, but has a very different meaning of "miss" to 2. and 3.
2. is far more standard than 3., but in informal speech we sometimes use feeling verbs in the continuous. The most famous example is the McDonald's slogan, "I'm loving it!"
So, 1. and 2. are correct (but very different), 3. is less correct