For me (and the simplistic stylesheet I'm using), it suffices to use
@page :nth(17) { @footnotes { max-height: 25%; background: yellow; } }
but there are some subtleties in what number to use (or what pages a given number will select), and that's why I suggest adding the "background:yellow" to the ruleset to make it clear what pages are being selected (to avoid confusion with any other rulesets that happen to be matching).
:nth() in Prince works the way :first does, in the sense that :nth(1) matches the same pages that :first does. So in many books, you'd need to give the page number relative to the start of the chapter rather than "153".
(Consequently, note that this would match the n'th page within each chapter; so you might want to use a special named page style that's used only for a single chapter, and change existing "@page chapter" selectors to "@page chapter, chapter3".)
Similarly, :nth() ignores changes to the 'page' counter, so even if you have the whole book in a single HTML file and aren't using named 'page' styles, you might still need to give a number other than 153 if your page numbering starts with roman numerals and resets to page 1 after the introductory matter.
Relatedly, if you've split your book content into several files, then you might find that :nth() doesn't count pages that aren't from the current file, even if you aren't using named page styles and page groups.
That's why I suggest adding "background: yellow;", to check that it's applying to the page you intend.
However, it would of course be better to find a better way of getting the pagination you want without the effort of manually adding and maintaining :nth() selectors. Maybe it's as simple as prince-footnote-policy getting applied somewhere, and (in conjunction with the limit on footnote area size) effectively forcing the footnote and its calling line (and hence the last three lines, given the value of 'widows') to the next page.
As I say, I do invite you to send me the stylesheet you're using, which makes it easier to understand its current behaviour and how to get the behaviour you want.