How do I make my manager understand that something isn’t doable no matter how much effort, time and perseverance are put into it?

———context———
I’ve been tasked in optimizing a process that goes through a list of sites using the api that manage said sites. The main bottle neck of the process are the requests made to the api. I went as far as making multiple accounts to have multiple tokens fetch the data, balance the loads on the different accounts, make requests in parallel, make dedicated sub processes for each chunks. All of this doesn’t even help that much considering we end up getting rate limited anyway. As for the maintainer of the API, it’s a straight no-can-do if we ask to decrease the rate limit for us.

Essentially I did everything you could possibly do to optimize the process and yet… That’s not enough, it doesn’t fit the 2 days max process time spec that was given to me. So I decided I would tell them that the specs wouldn’t match what’s possible but they insist on 2 days.

I’ve even proposed a valid alternative but they don’t like it either, admittedly it’s not the best as it’s marked as “depreciated” but it would allow us to process data in real time instead of iterating each site.