I progress it once but not animated (it's not from replay though) I didn't try to invite them via phone.
The general progression is:
1) Farm affection and move through story scenes until there's a non-animated sex scene with a girl
2) The next time you visit a girl (dorm for the students, home/workplace for side girls), there may be an option to perform the act from that scene again, this version will be animated, and can be repeated whenever you're in free-roam mode.
3) Eventually, you'll reach a point where a girl's next scene is shown in the list with a blue title. That's an invite-over event. The first invite over events are not animated, but again, future invite overs will show a sex act as an action, and that is a repeatable animated scene.
Note: When story progression makes a girl unavailable, because they're avoiding you, you're avoiding them, or you've sworn off sex with each other story-wise, repeatable scenes are temporarily locked out.