Thank you very much for all the details.
I have found the problem, it was a yet unknown bug with the recent version. It happened on single term searches, that is why the error was rarely seen in the logs.
I have replaced the faulty line in the main search query file for a temporary fix. For reference, the wp-content\plugins\ajax-search-pro\includes\classes\search\class-asp-search-cpt.php file was modified, you can keep a copy of it, if you use it on multiple sites.
I will of course fix this issue permanently within the upcoming release. The error should not re-appear now, hopefully.