This may be true for a subscription web app, maybe there is a bug and the customers can deal with not having a particular feature working correctly until Monday, you have a relationship with them and this is a mare annoyance.
Thinking in terms of an ecommerce or affiliate site, you have no relationship with those visiting your page. They're likely to close the browser or it the back button for the most inane reasons, you also have large adwords spend driving them to your site. Especially around Christmas time any issues could be a large potential revenue loss so yes I certainly would be dropping everything to fix any issues that arise.
Thinking in terms of an ecommerce or affiliate site, you have no relationship with those visiting your page. They're likely to close the browser or it the back button for the most inane reasons, you also have large adwords spend driving them to your site. Especially around Christmas time any issues could be a large potential revenue loss so yes I certainly would be dropping everything to fix any issues that arise.