Hi,
Can you please add temporary back-end and FTP access so I can check the problem?
These issues are super rare, and usually the cause is not directly in the search process, but somewhere during the post processing of the results. Things like: the plugin tries to request title and content fields for certain posts, but due to failed plugin hook WordPress can not complete the request and it bugs out. There are also custom codes (if you use any), too many filters used on the search – especially custom field and taxonomy related, those can create massive database joins etc..