How do I increase sudo password remember timeout?
Run sudo visudo and add this line:

Defaults    timestamp_timeout=-1


See man 5 sudoers. -1 causes the password to never timeout. You may change the number to whatever you like in minutes.

The man page for sudo says that sudo -v "extends the sudo timeout for another 5 minutes".

Running 'sudo visudo' instead of editing the file directly causes the system to validate the sudoers file before it commits the changes.  For instance, if you leave a stray character somwhere, when you save and exit, it will say "there is an error in the sudoers file, what would you like to do?" ... hence giving you a chance to go back in and edit.  This actually just happened to me 10 minutes ago.