There's a limit on the length of each product within the s.products string, but s.products itself doesn't have any limit that I'm aware of.
But browsers have a limit on the amount of data that they can send via a GET (i.e. what you see in the request URL) or POST (i.e. the request's payload) request. AA normally sends its hits via GET requests, so it's very likely that if you have a lot of products in your s.products string, then the resulting request URL to AA's servers has exceeded that browser limitation. And you can't do anything about that because the browser itself has that limitation.