Won't connect to more than one peer...
Peers?
The Blockchain for Android or iOS app is a mobile app that communicates with a back end / host.
Where are you seeing that it connects to peers? [Edit: I see, in the top left eventually appears a "signal bar" that shows "1 peers connected". I don't remember seeing that before. I think that is more like a yes/no ... if it appears then yes it has connected to the back end host (and will show 1 peer). If it cannot connect to the back-end host (e.g., no wi-fi, no data signal) then no "signal bar" ever appears.]
how do I save the petty coinage on here?
An encrypted copy of the wallet can be saved using the "Backup" from the Blockchain.info/wallet web site. You can also export the private keys from there to be imported elsewhere. An alternative client, MultiBit, can import the encrypted Blockchain.info/wallet backup.
But the mobile app doesn't work without a connection. So you don't need to store the "petty coinage", as it isn' t on the mobile app it is in your encrypted wallet on the host.