Not necessary. Mutiny is a private (unannounced) node with unannounced channels. That means are necessary to be online only in the moment of payment. Is true, you can get a force close channel in case you are paying a hold invoice and in the path you get a stuck peer with your HTLC. In that case is better to keep your Mutiny online until is confirmed / settled the payment, to avoid a force close.

Mutiny is NOT a public routing node - keep in mind that. Only public routing nodes must stay online 24/7.