I'm in a similar situation with a Physician LOR that I'm trying to obtain.
I shadowed with this Physician for 60+ hours, and at the end of the last day of shadowing he told me that he would write me a LOR and would do his best to help me out in any way needed. Well, two months later I'm still waiting on that LOR. Fortunately I volunteer in the Emergency Department and I see him frequently, and have been reminding him to write the LOR. After hounding him for two months he finally sat down to write the LOR he said he would write for me and now its sitting in my Interfolio folder.
The point of the above story is to be persistent and keep reminding your LOR writers to get your LOR done. Do understand that they are busy and have lives, but remember that they told you that they'd write you a LOR in the first place. If I were in your situation (and I was) I would send out another reminder, or an email asking of the status of your LOR. Hopefully all works out for you!
Best of luck!
-Wdoc