Out of interest to you ever get to the bottom of this other than having to swtich browsers? We have a rep with the same issue, where they have updated a deal stage and filling in the required fields, and are unable to save despite the button being visibile and in a clickable state (not greyed out).
No error message, just not response with the click. User has to restart browser (chrome) and is quite time consming. Have tried cache, cookies and browser is up to date.