There is no option, nor any way for the plugin to get exempt from the cache, only certain pages or files I believe.
But, I might have an idea why the issue is happening here. So, I remembered that the plugin has actually a fallback code whenever someone with a very old browser visits the site. What I believe have happened is, that whenever the cache was automatically cleared, the next visitor had an old browser and the default search bar was printed instead of ajax search pro – and that layout was cached by the cache plugin.
This would explain why only some of the pages have the default search bar visible.
What I did, is that I disabled this fallback programatically via FTP. If I'm correct, then this should no reappear anymore, once you clear the cache.
I will try to think of a permanent solution instead of this fallback – or maybe incorporate a switch to turn it off. I might ask a cache expert on how this should be handled in a better way for the next release.
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