How do I make sudo remember my password for longer?

There is timestamp_timeout option in your /etc/sudoers. You can set up this option to number of minutes. After that time it will ask for password again. More info in man sudoers.

And make sure you edit your sudoers file using visudo, which checks your syntax and which will not leave you with wrong configuration and inaccessible sudo.

There is a timestamp_timeout option in your /etc/sudoers...

Example: to get password remembered for 5 hours

Defaults        timestamp_timeout=300