I suspect the issue is bandwidth.  This particular server is on a connection that is limited to 768kb upload, and the messages range from 5 to 25 MB in size.  There is nothing I can do about the bandwidth.  Is there a setting somewhere to increase the time it will spend trying to deliver the messages?  Or maybe reduce the number it tries to send at once?  I am on Spam Filter v.4.2.4.844

With such a small section of the logfile we're unable to see the timestamp of when SpamFilter has initiated the outbound connection - all that is visible are the socket errors. The time interval that elapses from when the delivery is attempted to when the connection is dropped often can provide some clues as to the possible causes. If for example the time interval is pretty consistent (1 minute, 5 minutes, 10, 20) that could indicate fixed timeout on firewalls (yours or the recipient's), or disconnects caused by other antivirus/antispam software that could be examining the messages.

On SpamFilter's side, you can try increasing this parameter in the SpamFilter.ini file:

SpamFilter has a user-configurable limit for the amount of incoming SMTP connections. The limit for outbound connections is hardcoded to be equal to one fourth that threshold. If for example you set your maximum inbound Max SMTP connections to 100, SpamFilter will, as a consequence, have a limit of 25 outbound connections.