The American Mathematical Society has a email forwarding service for its members, which gives you a stable @member.ams.org address that you can update as you move. Something like this could be a good solution.

The American Mathematical Society had a email forwarding service for its members, which gives them a stable @member.ams.org address that they can update as they move. However, this email forwarding service is no longer available. Still, something like this could be a good solution.