Today I was going crazy because whenever I tried to update customer information from admin it was redirecting me to admin dashboard. It was working perfectly on previous server and on my local. After debugging for a while I couldn't find the solution for the issue at all.
I checked the required 'form_key' in the input that was ok because there was no custom work done and it was core file.
We moved to this dedicated web server running nginx so magento runs faster. After checking with hosting company they agreed to look into the issue and found the issue, it was related to fastcgi. According to them, they restarted all the fastcgi workers and it worked perfectly.
sudo allah restart {SSHUSER}_fastcgi
Just for reference: When creating a custom form in magento we need below code, so it doesn't redirect to admin dashboard or any other startup page set as default in magento admin system configuration section.
<input type="hidden" name="form_key" value="<?php echo Mage::getSingleton('core/session')->getFormKey(); ?>" />