Hi, a september rotation is no problem! You can get a letter in time, it ideally will be submitted to your school by the last week of October (giving the faculty 3 weeks to write it after your rotation ends). The programs upload the application Nov 1, and thats when they expect letters to be in your file. Like I said before, I got one from an October rotation, and it still was read in time for interviews.
The above posters are right, ask for more letters than you need, then target them appropriately. For example, a guy who is big at your school or in your state but not known nationally - his letter is good in those places, but dont send it coast to coast unless you must. If you have a letter from someone who trained at at particular program or with someone on faculty there, use that letter there.
Heres how I got the LORs from away rotations that made my application much stronger. Im adding this because its important to make your intentions known early in a visiting rotation, and even at your home rotation, otherwise they might not really notice you or your hard work and wont be able to write the best letter possible.
So, Im adding the approach that worked for me, so Im adding it because I think this kind of info would have been helpful to me last year.
On a visiting rotation:
I met with the letter writing target at the end of the first week of the rotation. So, that means I had to set up an appointment before I got there, since it takes a few weeks to ge an appointment with some busy faculty.
Anyway, in that meeting I introduced myself, told them how happy I was to have the opportunity to rotate at their program, why I was interested in their program specifically (2 sentences), and a one liner about my career goals.
I gave the writer a current copy of my CV at that time, and told him that my Chairman suggested I ask for a letter, because they thought that letter would be very helpful to my application. I then asked them the key question:
"Dr. ---, If I do a very good job on this rotation, do you feel comfortable writing me a strong letter of recommendation in support of my application to --- surgery?" So, this way they know who I am, they know I intend to ask for a letter, so they watched me a bit more the next few weeks, and ask residents about me perhaps. That gave me one week under the radar to get oriented, and three to shine.
At the end of that meeting I set up the next meeting with their secretary, during the middle of the last week onthe service - like Thurs (that way if it gets cancelled, just reschedule for Fri)
On the rotation, I tried to be early, read for cases, act interested (easy, because I am interested) have a positive attitude, dont say anything negative about anyone/anything if possible, try to relax and joke around a bit so residents can see that they'd like you on the team, know that nothing they ask you to do is scut during an audition rotation, try to anticipate their needs (pick up the OR schedule for tomorrow before asked or whatever) and dont leave until all the cases are done for the day and all rounds are over.
The last week, at the meeting, I brought another CV, in case they asked for it, and I told the writer: "Ive had a great experience as a visiting student here at xxx University, your program has exceeded my higest expectations, I am especially impressed by 1., 2., and 3. (briefly, like one compound sentence)"
Then I said, "Dr. xxx based on my work during this rotation do you feel comfortable writing me a strong letter of recommendation in support of my application to xxx surgery?"
This worked, even with a guy who supposedly does not write LOR for visiting students. Hope it helps.