When an ellipsis is used at the end of a sentence, then a period is placed before the ellipsis. In those cases, the sentence ends with four periods. For example:
“My brother lives in Florida. I talk to him every.…” His voice drifted off. “Well, it’s been a while.” Then he asked, “How about you? Any brothers or sisters?”
However, if the ellipsis indicates a pause but the sentence continues, then no punctuation follows. In these cases, you might be tempted to insert a comma or some other punctuation; but don’t do that. For example:
“Today, I had agents checking every site that our friends at the FAA identified as potential landing sites. We’ve checked …” he glanced at the tablet in his hand, “… eighty-seven percent of the sites so far. All negative. We’ll have the rest completed by morning.”
By the way, the Chicago Manual of Style specifies a non-breaking space between each dot in the ellipsis. But they also permit authors to use the ellipsis symbol of their word processor (Unicode 2026), which is what I recommend.
One last note. (It’s never that easy.) When you deliberately quote an incomplete portion from an external source, then you don’t add a period. For example:
I think every student should take a few minutes to listen to Martin Luther King’s speech: “I have a dream…” It’s quite an inspiration.