What actions trigger the need to obtain a new backup with Blockchain.info/wallet? Other clients, including Bitcoin-Qt, use a key pool so that a backup is still valid for a while.

Blockchain.info/wallet doesn't use a key pool.

After a backup of the wallet is obtained and archived, when would a new backup be needed?

[Specifically, does Quick Send send change to only existing addresses?]
A new backup is required after every Custom transaction in which the change is set to go to a New Address.

If you have configured your account with an e-mail address and have marked the checkbox for Automatic Email Backups a backup will be sent automatically via e-mail for each occurrence where a new backup is required.