I added some debug code and found that the error it was reporting is:
Message: Prepared statement needs to be re-prepared
I did some googling on that error and never found a good answer for the cause. I did see there may be an open mysql bug associated with it. It appears it may be a matter of increasing the "table_definition_cache" parameter on your database. But that may not be possible on a shared hosting environment.
I've "Fixed" the problem for now by updating the rsobj.php file on your server so that it doesn't use a prepared statement if no parameters are passed, and then updated your recordset to embed the parameter rather than pass it as a prepared statement. Unfortunately that will break inspection of the recordset on your page.
In the long term I may add a configuration option to the recordset to turn off prepared statements for people like you that run into this problem, but you will have to use the work-around for now. Make sure to download and save a copy of the rsobj.php file I updated in case you accidentally overwrite it.