You can keep it as long as you want, or set a specific length of time or number of messages to accept before terminating.
One of the most popular services for disposable email addresses is Mailinator. Anytime you need to use it, you can make up an email address, add @to the end of it, and an inbox will be created when a message is received.
Then, just choose an alias and a domain, click Save, and you're good to go.
And don't feel bad about using them—people willingly submit them to help others bypass restrictions.
I'm not talking about paywalls—I mean the sites that make you give them personal information to look at free articles or forum threads.
Most people are uncomfortable with this because a lot of these sites either spam you themselves, or sell your information to someone else who will.
All you have to do to access it is type in the address.
Obviously, since there's no password required, you don't ever want to use Mailinator for anything sensitive, but that's not what it's for anyway.