Irrelevant. That's the problem. The terms say X so they need to honor that. There is no verbiage about when you ask etc. That's the literal reason you spend 60 plus nights or X Dollars a year... to get certain benefits. When people allow excuses like I didn't ask at arrival etc, it makes them more bold in breaking the rules in general. The benefits and terms are already really hostile enough to the customer, so in the ways it is clear they need to honor that. Full stop. I'm not saying you can't and shouldn't be gracious in working with a hotel when certain things are difficult for them or you don't really need or want etc, because plenty of good hotels certainly still go above and beyond. However if at the end you really need a benefit like late checkout and it's one of those that's very very clearly spelled out, then if push comes to shove, they need to give and if they don't, you need to elevate it.
As mentioned at the start of my post I'm not debating that the request is supposed to be honored. (Unless there is some buried technical detail we just don't know, and I doubt there is).
Not often that I needed to, but I've pushed back and the FDA folded. I've pushed back and the FDA relented but housekeeping went into some form pf passive-aggressive compliance by going out of their way to make noise or keep knocking on the door (which I found annoying but strangely amusing, so I stayed later than needed just because). I've push back and they requested I move to a departure room (fully acceptable to me). I've pushed back and had "the manager" lie like a rug that such a benefit even exists. I've pushed back and lost and later contacted the real GM and received apologies. Sometimes I really didn't care, or it was so obvious the FDC was caught in the middle that I let them off the hook as an act of personal mercy.
Not that many occurrences in any form, but most of the limited flat refusals were when my situation changed day of departure. Which is why I asked what the timing was. It is helpful to know more detail not less, and we still don't know what reason the OP was given for (implied) denial of their request.