Devise rememberable is supposed to set a remember_user_token cookie on the client so that even when the session cookie is deleted, the user does not have to log in again.
t.rememberable is set in the create_users migration and devise :rememberable is present in the user model.
The reason for this is because of the way jQuery mobile handles checkbox inputs and the labels for them when reformatting the page. The simplest fix is to install the devise views in your project by running rails g devise:views. Then in the new.html template for the session controller, switch the order of the checkbox and the label so that the label for :remember_me comes after the checkbox.