It depends on when this wallet was created. Quite old wallets used a pool of independent private keys. IIRC, Bitcoin Core would maintain a key pool of 1,000 unused keys and replenish new random keys as the wallet received payments. Under this wallet system, backups of heavily used wallets would eventually become obsolete when all keys in the original backup had received funds and new payments were received to addresses generated after the backup was created. IIRC, the default key pool size may have been increased to 10,000 at some point, but the general problem persisted.
In 2016 with Bitcoin Core 0.13.0, deterministic key generation based on BIP 32: Hierarchical deterministic portfolios has been added to the Bitcoin Core wallet. If your wallet was created with an earlier version, you may have deleted the only copy of your keys and have no recourse. If your wallet was created by Bitcoin Core 0.13.0 or earlier, you should be able to recover your funds by rescanning the blockchain.