How to exclude nonces from cached pages?

I’m trying to use Ivory Search which has an ajax search function. But the problem is that a nonce expires and so on cached pages the ajax search eventually stops working.

See here: https://www.ads-software.com/support/topic/ivory-search-stops-returning-results-after-a-few-days-of-cache-being-active/#post-17110382

and here: https://www.ads-software.com/support/topic/ajax-search-stops-working-due-to-caching/#post-18346826

The people at Ivory Search suggested: “Please contact the WP Super Cache plugin support below to know how to exclude is_ajax_nonce from the cache.”

Is this possible?

To be clear, I don’t want to exclude posts/pages from caching that use this ajax search, as I have the search bar set to appear in the sidebar of every post/page.

Thanks

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