No, it stakes while you are online. If you quit and restart after a few days, it will catch up where it stopped. So there is no need to stay online 720 hours non-stop.

Also, you can stake with a locked wallet, you can read about this in the FAQ's at the "wallets" menu item on paccoin.net. It says:

How to unlock the wallet for minting only?
Go to Help > Open Debug Window and there type:
walletpassphrase “your-password” 9999999 true
Please notice that your password is the one you created when the wallet was encrypted.