Protocol for checking in on a letter of recommendation more than once?
No, it will probably not be considered rude to repeatedly ask for a letter.  The professor agreed to write the letter and clearly understands what it is and why you need it.  If it is a few days before the due date, they haven't turned in the letter and they haven't responded to your last email, they evidently need the repeated reminders.  I honestly think it is more likely that they will be sincerely grateful that you are helping them to complete a task they agreed to do than that they would be even a little bit annoyed with you.  But if they do get a little bit annoyed with you -- okay, maybe that's what helps them write the letter.  It would be highly unprofessional to respond to this kind of behavior from a student by writing a worse letter or not writing it at all, and I honestly don't know of any professors who would behave in that way.

Finally, let me say: faculty turning in letters late is such a common thing that in many circles at least there is a de facto grace period for faculty to turn in letters which is up to a week or two after the actual, posted application deadline.  As a student it is hard for your mind to really be eased by knowing this, I expect, but it helps to understand the faculty mentality: if I turn in a letter two days after a deadline, I would actually be annoyed if it were not considered.  (And I would know it was my own damned fault, but I would be annoyed anyway.)  

Good luck, and keep at them.