Crime rates reduced during the time stop and frisk was implemented. But when it was removed, crime rates remained low:
https://www.brennancenter.org/media/5670/download
Strongly suggests correlation but not causation.
Yes, crime decreases tend to stick.
Chicago started with similar conditions as NYC (30 murders per 100000 in 1991), but they didn't have no-nonsense mayors like Bloomberg and Rudy. So its murder rate now is still 5 times that of NYC.
Broken window policing and stop-and-frisk absolutely worked. Stop-and-frisk was found to be unconstitutional, but it also was highly effective.
Or… criminals were caught and remained incarcerated leaving rates low. A large part of crime is committed by repeat offenders. Catch and imprison them and crime drops. This is well supported by data.