The Infamous "Remember Me" Checkbox
Persistent Login Cookies ("remember me" functionality) is a danger zone; on the one hand, they are entirely as safe as conventional logins when users understand how to handle them; and on the other hand, they are an enormous security risk in the hands of careless users, who may use them on public computers and forget to log out, and who may not know what browser cookies are or how to delete them.
Systems like Jasper can't afford to have any accounts hacked; therefore, there is no way I can justify having persistent logins.