When a customer clicks to update the quantity in their basket, the one click checkout button disappears from the minicart view.
Can you check if there is some error on your browser console?
Also, what happens if you check the same using the Luma theme?
I'm not sure but I guess you're using Magento 1. If that's the case, can you check using RWD theme to try to understand if the problem is the theme or maybe a module?