I sent snail mail too, one replied with a phone call to set up a time and day etc.
Another DO that I was very interested in shadowing never responded so a few months later I brought a letter in an envelope and hand delivered it at his office-he ended up writing my LOR and was a great mentor. They are very busy so give them some time to get the letters and get around to calling you, and if you don't hear from anyone in the next few weeks or months perhaps hand deliver a couple of letters to offices.
A lot of time its a shot in the dark who replies and who doesn't so make sure you send out letters to 5+ docs so you have a good chance at one responding.