I am working on a Lemmy client and have noticed that the Login system is secure, but it isn’t very robust. Usually, there is something called a “refresh token” provided that automatically verifies users and lets a user stay logged in indefinitely. Lemmy doesn’t have that implemented at this time, so eventually you will be logged out by your browser as a security measure when your cookie expires and you will have to log in again. For Safari, the maximum time is 7 days before you are logged out.
So, until Lemmy implements refresh tokens or similar, this will probably be how it is on most browsers and Lemmy clients.