At my school the reference writers themselves are working to a deadline, independent of the students really. So, what with all their own palnning, marking ,parents' evenings and so on, I imagine most either leave it until close to the deadline or spread it out. Just because they have done some does not necessarily mean it wil ahve been passed on to whoever does the final bit... a typical worload at my school would be one teacher doing about 25 - 30 references, so it is a big job.
That could potentially explain what seems to be a delay. I don't think that's how all schools work but is certainly true of large schools on the whole. The references at my place are completely independent of anything the students do : they are written without sight of the rest of the form. Is my understanding.