How long should one wait for a reference before writing to the course convenor? I am getting a little worried about my PhD application. I submitted it three weeks ago with reference requests going out to Prof A and B. Prof B wrote to me the same evening to say it would be done asap, and Prof A didn't respond, but that's fine. Three weeks later and Prof A has written back and completed the reference, though nothing so far from B. I have written to B with a polite reminder but they haven't written back. How long do people take on average to get these things across and should I be concerned? I know these academics are very busy but at the same time this is the only thing holding the application up. Should I write to the convenor about my concern if this goes on for a couple more weeks? What other ways could I politely encourage a response?
I'm going to answer this question myself for the benefit of people who may stumble upon this in the future. 

In the end I didn't email the convenor, but I phoned the Prof in question. I initially thought maybe I needed to give it longer than three weeks and I was being impatient, but it turned out that they totally understood and said they had been very busy but of course they would do it. They ended up submitting the reference the same day. To those people who may be in a similar situation: don't be too shy about phoning or visiting your professors for this reason. They understand the necessities of getting it done and done in good time, but understandably get waylaid by priorities.