Zello uses circular buffer to store history on devices, which means the oldest messages will be deleted to make room for new messages whenever the storage limit is reached. The storage size of history for audio, texts, and images can be customized using settings on your Options>History screen. You can also disable History entirely from that screen. This does not prevent other users from saving history from a channel or group, however. 

Note that audio messages, images, and texts are only saved on your device and not Zello's cloud servers (with the exception of shared messages). Messages that are deleted or drop off cannot be recovered.