I am currently preparing for the graduate school application. I was asking for reference letter from one of my Math professor who knows me well. I took classes with him for twice, went to his office hour frequently, and we were talking to each other for many different things other than the class/grades. He was very caring and helpful all the time. I asked him if he will be willing to write me a ref letter for graduate school programs, and after nearly 2 weeks, I got an reply said yes, he will be very willing to. But he reminded me that he is a very slow people and I will need to remind him at least two weeks before the deadline. After that, I sent him about some supplementary materials such as my CV/personal statements to help him write the ref letter and ask if he will need more information from me, I have been waited for more than two weeks, and I repeatedly sent reminder emails for three times, but I still got not reply from him. I went to his office, but because of the pandemic thing, he was not there. I am so nervous and concerned and not sure what sure I do next? I was calling the Math department secretary to ask her to send an email to remind him to check the email, but I also did not get any feedback from him yet. Does anyone have any suggestion for me??? I will be really appreciate for that! Also, if I got reply from him, should I politely ask him to give me his phone number in case I might not be able to contact him through email again. I am not sure if this is polite but if he cannot reponde me in time in particular when the deadline gets closer, that will be very awful :(
I suspect that he knows of your concern and will come through, though at the last minute. But "repeatedly sending reminders" is also "being a bit of a pest". Most people will forgive you for that, but not all.
But, he has other things to do and needs to think about what to write on your behalf.
Phoning him will just make it worse, interrupting his schedule.
So long as he knows of the deadline you should be fine. A message a few days before the deadline wouldn't hurt, mentioning your eagerness to know.
But replying to constant reminders just slows down the process, so they are often ignored. It is a mistake to make him less efficient than he could be. Relax for a bit. There is little incentive for him to rush it unless the deadline is immanent.