Explanation

The clause requires a reason for stopping seeing her, and because she moved to the city supplies the direct causal link. Because is the standard causal conjunction introducing the reason for the main clause action. For can introduce reasons but is formal and archaic in this position, while as long as expresses a condition and no sooner than misuses the correlative, which requires no sooner with than and inversion. The cause-and-effect relationship makes because the natural choice.