Ajax search stops working due to caching

I’m using WP SuperCache. The ajax search works well initially, but after a while the ajax stops loading (i.e. the load image shows but no search results popup).

I see this topic here, with a solution related to ESI: https://www.ads-software.com/support/topic/ivory-search-stops-returning-results-after-a-few-days-of-cache-being-active/

But I don’t see an option for this within WP Supercache. Is Ivory Search incompatible with WP Supercache, or is there another solution I can use to fix this issue?

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