There is no time between photons for which the interference pattern goes away. Even if you send in one photon at a time, and wait until after it has been detected to send the next one, you will still see the detections build up to make an interference pattern.
You can find lots of pages on the web describing experiments where the time between photons is large enough that they do not affect each other. I used the image from this page at Princeton as illustrations in my book, but there are lots of others. You can also do the same thing with electrons, which again, has been done many times, including this version from Hitachi which includes a nice movie of the pattern building up one electron at a time.