It takes a lot longer than a few minutes for it to speed up. Sometimes I come back the next morning and it's still running in the 2K-5K per second range.
I thought it was peer-to-peer, I don't think they're even keeping copies of the data.
BTW, I'm running the 0.8 version, it's supposedly faster, but so far -- doesn't seem to be.
I don't think they're using peer to peer. From what I know they use local syncing on the client and the content is uploaded via SSL, and stored encrypted on EC2 storage.
It is peer 2 peer within the lan ( see options - enable lan syncing ). This is great for companies that manage shares though dropbox. This way you don't have 40 people download the same bit.
Usually when this happens to me, I close Dropbox (quit the application), wait a few minutes, then re-open it. Typically that fixes the slow speed and ramps it back up to capacity (I'm on Verizon Fios).