Hi!
Can you check the versions of buddypress on both sites? Maybe one of them is an older version?
Are the two searches configured exactly the same way? You should check the grouping options on the advanced search settings panel. I’m not sure that can cause it, but I have seen disappearing results because of that once before.
Is there any buddypress related plugin installed on the websites? Maybe the search is incompatible with that plugin?
If you can’t solve this, can you provide temporary ftp/admin access, so I can do a deeper debugging on the affected site?