I already answered this in a PM, but will post it here as well for reference:
You can use the "Save message" button to remove a message from the Inbox and move it to the "Savebox"--but there is a limited amount of space there, as well. Personally, I only have about 10 messages that I saved for whatever reason. I delete messages from my inbox pretty regularly.
Other than that, there is really no way to save messages except for what Tracy stated above.