Exactly what information is stored in your wallet? Is it just your public and private keys? If you back up your wallet, can you load it into another copy of the program and send bitcoins from there? And if you back up your wallet, then gain coins, and restore from a backup, will your coins still be safely stored in the blockchain, or will your balance be as it was when you backed it up?
Your bitcoins will be stored as long as you have the accompanying private keys to the address where the bitcoins were sent to. You can receive bitcoins to an address without ever connecting the wallet to the internet.