Do colleges save your application essays from when you previously applied?

They keep your entire application for a period of time (I want to say 2-3 years is typical, but don't know if that's right).

Even if they knew you were reusing an essay, a college might think it was lazy of you but I don't think they would disqualify you for it. It's not the same thing as turning in the same paper for two different classes for credit; that's academic dishonesty because writing an original paper is expected as part of the learning process and grading criteria for each class. For college applications, it's just a sample of your writing, and it's understood that you will use the same essay when applying to multiple colleges.

That being said, your writing might be better now than it was then, or the circumstances you write about may have changed, so it may be worth revisiting for other reasons.

Technically, since so many applications are digital now, colleges could save past applications but they probably won't. Colleges get so many every year, there would be almost no point after they've accepted who they want to accept and denied those that they wanted to deny. Chances are they probably at least save a list of names who applied for their records~but it's not like they'll remember you or your essay (unless it REALLY stood out and you got the same application reader).

Write a new essay. Especially if you were denied from that school the first time.

I don't know but is it worth risking it? I would just write a new one.