While the update itself won't bring your ringtones back from the dead, Apple has another way to restore missing purchases: After you install the update, follow Apple's ringtone restore link (itunes.com/restore-tones) on your device, which will redirect you to iTunes. Follow the on-screen prompts from there.
To install the update, go to General > Settings > Software Update if you'd like to install the update over the air, or connect your device to your Mac to update via iTunes. For more security info and software updates, check out Apple's security updates page.
Leah Yamshon