A week or two before you cancel your current ISP to move, sign up for a free-mail account. Next, send a single message to your forwarding service advising it to forward your mail to the free-mail account. You can also make the change at the web site. After you arrive at your new post and establish a local dial-up service, change your forwarding address and return to using your favorite email program. A third strategy is to register your own Internet domain name, but it's a bit more expensive and the available names are quickly disappearing.
Costs are considerably more for storing email and hosting a web site.
All of these strategies help you avoid losing emails. The first is less expensive, but the second gives you more choices and convenience. The third gives you the same benefits as the second option, but with an added expense for the domain name of your choice.