99% of the time that there is a failed upgrade like this – which is not that often – it is caused by another process hijacking the AJAX request so that the data that gets returned is not what Simple:Press is expecting and thus suspects an error condition.
I am concerned, however, with that Notice which is not, itself, an error, but is an annoying message that may be tripping things where they should not. Notices like this should not be sent to the display but should be logged which means you should really be changing your php ini file to stop these. It is bad practice to allow them to display on a live website. I am not sure, as I have not seen it happen before, but that could be the cause of the erroneous return data.
I can think of three possible solutions. The first – and the most correct – would be to fix your php environment to not display notices and warnings as it should not. This should be done in any case. (Of course you may just have WP_DEBUG turned on on the WP config in which case turn it off)!
The second would be to remove the SP tags plugin from it’s folder – run the upgrade and then out the files back and reactivate. That should work but if your system is showing notices there may be another one lurking in the depths!
The third option would be to make manual edits directly to your database (quite simple edits using a tool like phpMyAdmin) to spoof the upgrade. The upgrade script from 5.5.1 to 5.5.2 would be safe to ignore. I can walk you through this if this is your preferred option.