Mass Effect 2 how to regain the loyalty of Jack?

You have to have a very high amount of Paragon/Renegade in order to gain her loyalty back. You need slightly less of either to resolve their fight without loosing either person's loyalty, so it is likely that you aren't going to be able to get her loyalty back for a while.

Edit: Check out here and search for regain to find the sentence saying you can regain loyalty: http://masseffect.wikia.com/wiki/Loyalty

Edit 2: I said you need very high paragon/renegade in order to get her loyalty back. You should also have noticed similar choices during their fight.

You can't. What you would need to do is go back to a save game BEFORE you did either Jack or Miranda's loyalty mission and do other missions instead. Eventually when either your paragon or renegade score gets to about 75% or so, go finish Jack's mission. Then when the fight breaks out you'll have a renegade/paragon option that will let you keep the loyalty of both.

If you already lost it, there is no way to regain it.

Wow I played and beat Mass Affect 2 and also got extra missions from dlc and this never happened to me. But its good you sided with Miranda because shes more usefull then Jack and also gets better later in the game.

Yea