On mobile devices in particular, different apps (such as Facebook and Twitter) use different browsers. While it is necessary to log in for each app/browser, if you leave the “Stay logged in” box checked, your credentials should be saved in that particular app/browser.
If you are on a shared computer, you should avoid storing your user account/password in the browser. However, if it is your personal computer or a secure individual profile, you can allow your browser to save your login information. Similarly a password manager, such as 1Password, Dashlane or Last Pass are also secure alternatives.
※If you are using the Safari browser, due to browser specifications, you can only stay logged in for a maximum of 7 days. We apologize for the inconvenience, but you will need to log in every 7 days or consider using a different browser (such as Google Chrome or Microsoft Edge).
See also: [ What is the domain I should save in my browser? ]