Comment on How to Update WordPress Themes by SEO Dave.
If your hosting limits the disk space or your PHP upload setting (forget what the setting is called) is below 6mb you are going to run into problems.
That error sounds like your hosting is running out of space between the combination of temporarily uploading the zip file (6MBs) to your site plus extracting it (10MBs), so you temprarily need around 15MBs added to whatever is currently on the site (including the old Stallion files that will be deleted after the update, so 20MB to be safe).
I’m uploading 95% of my sites using FTP, I’ve used the custom-widget.php file a lot so some of my sites have a custom file I don’t want to upload over. I would check what your host allows you to upload and use FTP, comparing the extracts file sizes of Stallion 6.0.1 to 6.1, the update is a few MBs bigger, so if using FTP be sure your host allows you 5MBs more than already used and you’ll be fine..
I’ve spent all day updating sites, I’m going through them alphabetically and at the Vs, so almost there :-) Not had any major problems.