I take it this is happening because the computer is getting a new IP address?
As a result, the SPF check fails, and the message bounces.
This is just one example how short-term DNS inconsistencies can lead to temporary SPF failures and bouncing of legitimate mail.
Some nice people have taken the time to write auto-updating clients for the Dt DNS service.
The current specifications are available if you would like to know how to write your own updater.
Like I said I'm kinda new to the field and just trying to work through this problem.