Bitcoin wallet not syncing
New blocks are continuously being created (about once every 10 minutes).
So if you don't leave your client continuously connected, then when you do connect it will be out of sync and need to download and verify new blocks.
There are SPV (Simplified Payment Verification) clients (e.g., MultiBit and Bitcoin Wallet for Android), client-server clients (e.g., Electrum), and hosted (shared) EWallet web services (e.g., CoinBase, Paytunia, and others) -- each of which either lessen or eliminate the need to sync.
One method that brings the convenience of an EWallet but keeps the private keys local and not stored with the provider is