If after restarting the APU subsystem, the Jupyter notebook does not reconnect,wait for around 120-150 seconds and try hitting refresh (Normally F5 key).
If the petalinux image is configured to have dynamic (static in tutorial), then enter the new ip address (if the board ip is reassigned) after each reboot in the browser.
If after restarting the APU subsystem, you are prompted for the key again, make sure that cookies are enabled in your browser.