Do you mean the primary ArcMap window, itself, or something like an attribute table that you've dragged out to a separate window?
If it's the first one, that's certainly odd behavior and I don't have any suggestions. It sounds to me like something is bringing it forward, not that it's staying forward (subtle but important distinction). I'd recommend reaching out to ESRI support.
If it's the second one, that's essentially by design, I think. See below for more. N.B. I'm using Pro, now, but the behavior I describe below was the same back when I used ArcMap, and for basically every program that has "child" windows like this.
For example, I have two monitors. Generally, I keep my main instance for whatever I'm working on open in the monitor on the left. Anything I need to reference goes on the monitor on the right. Sometimes that second monitor might be an attribute table, sometimes it's another Pro project, and sometimes it's some other file entirely, sometimes it's some combination of the above. The important one for this discussion is when the second monitor has an attribute table or anything else that comes from the primary project (i.e., it came from the left window, and I dragged it over to the right).
Say I had a PDF open on the right hand side that I was referencing, but now I've opened an attribute table that is on top of the PDF. So far, so fine, because when I click Pro on the left window to do work, I'm referencing the attribute table on the right, and both are on top. But let's say I need to go back to that PDF for something. Instead of closing the attribute table, I just click on the PDF to bring it to the fore. Now I'm looking at the PDF on the right and Pro on the left. Then I click back to Pro (or ArcMap, in your instance) on the left window to resume working. Wait, where'd my PDF go? It's now behind the attribute table, because as far as Windows is concerned, that attribute table on the right and the main project on the left are the same thing. So it just brought a single thing to the fore of both monitors.
Because of the way Windows (and most other OSes) handle, well, windows, you're always going to get that behavior if you have "child" windows that belong to a primary window somewhere else.
