How do you write an ellipsis following an abbreviation?

Consider the following sentence (off of the top of my head just to illustrate an example):

I hate the N.C.A.A....but I understand that it's a necessary evil.

When following an abbreviation with an ellipsis, should you have three or four dots? Should the period following the last "A" in "N.C.A.A." be omitted or included, given the ellipsis right afterwards?

The technique you are using is actually called aposiopesis. It's when you pause in a sentence for an effect.

There are two ways of doing an aposiopesis, using an ellipsis or an em dash.

However, when using ellipsis for aposiopesis after abbreviations, could be quite tricky. Ellipsis when used at an end of a sentence always have four dots, three-dot ellipsis and a period. So I would assume that is what is done for the period after abbreviations.

But there's always the alternative of just using an em dash if unsure.

In general, you treat the ellipsis as a single character that just so happens to look like three periods. This means that if the ellipsis comes directly after an abbreviation, you'll end up with four dots in a row. Same if you end a sentence with an ellipsis.

Peter Morgan is right, though, that in most cases an ellipsis looks better if there are spaces on either side of it. So in practice, the only time you're going to end up with four uninterrupted dots in a row is at the end of a sentence. (And even there, if you use an ellipsis character [Windows Alt-Num+0133, Mac Option+Semicolon, Html …], the actual appearance will depend on the font: …. and .... look quite different in the editing window [monospaced font], but identical in the preview [proportionally-spaced font], for example.)