Above all else, your data needs to remain secure. This is why Twitter requires all third party applications to use OAuth to connect to their accounts — it prevents applications from storing users’ Twitter login information. As such, we don’t store the authorization token returned by Twitter when you login.
Theoretically, we could store the tokens with each account which would allow you to remain logged in but it presents a security risk. If a database were compromised, Twitter login information for ALL users could be accessed. Although it’s highly improbable that this could happen, it’s not impossible. And as many of our users have expressed, they’d prefer to have a slight inconvenience if it means they’re accounts are more secure.