If you want to maintain access to your e-mail for the long term, take some time to think through what you really want to keep and let go of the rest.
Then make a plan for keeping those kinds of e-mails you really need.
These links can help you make a plan!
Tips for working through your specific e-mail situation
A great 2-page PDF guide defining e-mail lingo and providing step-by-step tips
Keeping Personal Electronic Mail (excerpted from the Library of Congress, 1.8.2017)
Identify all your e-mail sources
Decide which messages have long-term value
Export the selected messages
Organize the saved messages
Make copies and manage them in different places