If I unlock an encrypted wallet for 359711509437336256 or less seconds, I can sign transactions with it:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336256
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
      "complete": true

But if I unlock it for 359711509437336257 or more seconds, it appears to have unlocked but I can't sign any transactions:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336257
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
    error code: -13
    error message:
    Error: Please enter the wallet passphrase with walletpassphrase first.

I don't know the significance of that number. It's nowhere near a power of 2.

I was trying to unlock the wallet effectively "forever", so put a big number. If I use too big a number (2^63 or more) I get an error message `JSON integer out of range` but for numbers between 359711509437336257 and 2^63-1 inclusive I get no error, but no actual unlocking.
{
    CWallet * const pwallet = GetWalletForJSONRPCRequest(request);
    if (!EnsureWalletIsAvailable(pwallet, request.fHelp)) {
        return NullUniValue;
    }
    if (request.fHelp || request.params.size() < 3 || request.params.size() > 6)
        throw std::runtime_error(
            "sendfrom \"fromaccount\" \"toaddress\" amount ( minconf \"comment\" \"comment_to\" )\n"
            "\nDEPRECATED (use sendtoaddress). Sent an amount from an account to a bitcoin address."
            + HelpRequiringPassphrase(pwallet) + "\n"
            "\nArguments:\n"
            "1. \"fromaccount\"       (string, required) The name of the account to send funds from. May be the default account using \"\".\n"
            "                       Specifying an account does not influence coin selection, but it does associate the newly created\n"
            "                       transaction with the account, so the account's balance computation and transaction history can reflect\n"
            "                       the spend.\n"
            "2. \"toaddress\"         (string, required) The bitcoin address to send funds to.\n"
            "3. amount                (numeric or string, required) The amount in " + CURRENCY_UNIT + " (transaction fee is added on top).\n"
            "4. minconf               (numeric, optional, default=1) Only use funds with at least this many confirmations.\n"
            "5. \"comment\"           (string, optional) A comment used to store what the transaction is for. \n"
            "                                     This is not part of the transaction, just kept in your wallet.\n"
            "6. \"comment_to\"        (string, optional) An optional comment to store the name of the person or organization \n"
            "                                     to which you're sending the transaction. This is not part of the transaction, \n"
            "                                     it is just kept in your wallet.\n"