I generated a signed transaction using MyEtherWallet on an air-gapped computer, and used it to successfully send a transaction. Does anything prevent the signed transaction from being reused?
Each transaction requires a nonce (or sequence counter) value from your account. For each transaction you submit, the nonce is incremented. This is intentional to prevent replaying transactions.
So no, you cannot send the same signed transaction again once it has been accepted by the network because the nonce value will not match.