Failed WordPress Upgrade – site crashes

I seem to be having trouble with upgrading wordpress on only one of our many websites. I routinely do upgrades as they become available and it is simple for all the sites except this one at:

http://www.dentalclinic.com.ph/

We have other .ph wordpress sites that do not have this problem.

When the site goes down after upgrading wordpress, this is the message shown:

Fatal error: Call to undefined function get_option() in /home/smiles/public_html/wp-admin/admin.php on line 32

After the site goes down, I do a manual upgrade. It is especially important to prevent this site from going down because this site belongs to one of our clients. Is there a setting or something that can be done to prevent the crash without doing a manual upgrade? A setting perhaps?