The most likely reason that your Doctor friends are not receiving messages from us that emails are being delivered to their Junk or Spam email folder.
Ask them to find the emails with subject 'Request for recommendation' in one of these folders and then mark that email as Not Spam.
If recommendation is not visible even after 3-4 days (usual time for approval) of submitting it, it means the recommendation was not submitted properly. The proper way to submit recommendation is to click on Write recommendation button in email received. In no circumstance, recommendation should not be sent by replying the received email.
You may request recommendation again by submitting the form through your Account Page.