If you check the Save checkbox on the authentication or private key password fields, the app will store your password in an encrypted form, however a determined attacker with physical possession of the device would still be able to recover the password with some reverse engineering.
Currently, the best options for security are to avoid saving passwords, and to use the Android Keychain as a repository for your private key (see below).
The Android developers are in the process of implementing an API for secure storage of passwords that will leverage on the hardware-backed keystore and master device password, however this development is not complete as of Android 4.2. This approach will protect saved passwords even if the device is rooted. When this development is complete, we plan to support it in the app.