Here's a basic example (not actually the way most deterministic wallets work, but a simplified example): To generate a private key take SHA256(string + n), where n is an ASCII-coded number that starts from 1 and increments as additional keys are needed.
So for the purpose of this perhaps overly-simplified example... When such a deterministic wallet is scanning the blockchain, how does it determine the value of 'n' at which to stop scanning? Is there not a tradeoff between efficiency (stop scanning some time before 'n' reaches infinity), and potential leakage of funds?