Thank you for all the details, I might have been able to find why. The links were indeed not returning the correct page layout.
It took me a great amount of time, but I finally found what the problem was. Simply, whenever Ajax Search Pro initialized the wordpress file system, the pages went broken, whenever they were saved.
My guess is that there might be an issue wit the file system API, if it's initialized sooner in certain conditions. It might have to do with a speific server configuration and maybe php configuration as well – as I was not able to replicate this same problem on my test environments.
Anyways, the fix was very simple, I just had to remove the WP filesystem API initialization code, and replace it with native PHP code, and it all seems to be working correctly now. If any of the pages is still broken, simply disabling/enabling the plugin should get rid off that as well.
I will make sure to add this solution permanently to the upcoming update, as it does not affect the search, and prevents this possible issue as well, in case someone else encounters it as well.Best,
If you like my products, don't forget to rate them on codecanyon :)