Try changing the transfer_timeout setting in settings.php. I know I set that to 0 half a year ago or so to let people download through my proxies.
If I had to guess I'd say a curl upgrade, or some other component being used changed the behavior of how that worked.
I've been doing some testing and I moved to a setup involving squid in front of lighttpd and I still saw the issues. I changed the transfer_timeout and it seems to be working better since yesterday afternoon.
It looks like there may be a bug somewhere.