I kept my response simple. Make sure to check out the video to hear how I would and have approached this. The answer is gratitude and people skills. Be thankful for their willingness to recommend you. Don't hassle them. They have 100 other things to do and you're not one of the top priority items. Don't take it personally. They are running a company and although they want to support you, finding the time is difficult. This is how I do it.
At any point in the process, the letter may be complete. Thank them. If the letter is not complete after step 3, give them at least 2 weeks and then follow up again. Be persistent. Be grateful. Be professional. You'll get your letter of recommendation!