All channel info/messages is saved on relays. The app just doesn't know which channels you'd like to download to the phone. For that to work, just keep the list of note IDs from the channels you want to see in a file somewhere.
Discussion
A channels == My Followings? I only just installed Amethyst at another Android device and I see all my 12 Followings in profile. I don't see any difference between first device Amethyst :) Same profile, amount Followings and Followers, same my tape :)
And I only logged through a private key
Maybe one of the relays wasnt available or the older app still has information from older relays?
It seems to me that we don't understand each other. Maybe because my native language is not English. I thought you meant to say that I have to manually save my lists of subscribers or "Followin" tab in Profile (called by you channels?) before exiting from the Amethyst. Instead, I decided to log in to the Amethyst with my key on another device. And as I did, all my subscriptions were restored (Following/Folowers tabs). In the last message, for some reason, you assume that there was some old information at relays. Why? Everything seems to be working fine. It seems to me that it is not necessary to save the channel list in order to exit and re-enter from the application. It is enough to have only a private key. Right?