Quick background: I am applying to grad school and asked two professors from undergrad and a current work supervisor for letters of recommendation and they all said yes. I asked about a month and a half out from the due date, gave them all updated resumes/statement of purpose/any other information or paperwork they asked for. My supervisor got the letter finished rather quickly and sent me an email to let me know. About two weeks out from the application due date I sent a brief reminder/follow up email to my two professors ("just a reminder this is the due date, let me know if you need any more information" etc). Last week (about a week before the due date) one of the professors got back to me to let me know she had finished/submitted the letter. The due date for my application is in a few days and I have not heard from the second professor.
My question is: I have already sent an initial follow up email for a letter of recommendation. Is it considered rude or pestering to send a second email? I have no qualms on how to word this email - I will still be very polite and accommodating of course - but I understand professors are very busy. I don't want to be a bother but also I need this third letter of recommendation and this professor willingly agreed to help me. Is there a protocol for a second round of follow-ups for letters of recommendation?