Thanks for the feedback!
Based on your description it's possible 2 things causing the problem:
1. The plugin is malfunctioning at some point and getting perhaps incorrect post IDs (or something related)
2. Or/And the theme search.php or some hook does some filtering of the results – which causes the empty pages and the pages with less than four results.
Unfortunately it's impossible for me to tell where the problem is exactly without debugging through the search code first and checking the theme search.php file as well. If you can add FTP access I will gladly take a look and suggest a fix if it's possible.Best,
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