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.
if (fByAccounts)
    {
        for (const auto& entry : mapAccountTally)
        {
            CAmount nAmount = entry.second.nAmount;
            int nConf = entry.second.nConf;
            UniValue obj(UniValue::VOBJ);
            if (entry.second.fIsWatchonly)
                obj.push_back(Pair("involvesWatchonly", true));
            obj.push_back(Pair("account",       entry.first));
            obj.push_back(Pair("amount",        ValueFromAmount(nAmount)));
            obj.push_back(Pair("confirmations", (nConf == std::numeric_limits<int>::max() ? 0 : nConf)));
            ret.push_back(obj);
        }
    }
    return ret;
}
UniValue listreceivedbyaddress(const JSONRPCRequest& request)
{
    CWallet * const pwallet = GetWalletForJSONRPCRequest(request);
    if (!EnsureWalletIsAvailable(pwallet, request.fHelp)) {
        return NullUniValue;
    }
    if (request.fHelp || request.params.size() > 3)
        throw std::runtime_error(
            "listreceivedbyaddress ( minconf include_empty include_watchonly)\n"
            "\nList balances by receiving address.\n"
            "\nArguments:\n"
            "1. minconf           (numeric, optional, default=1) The minimum number of confirmations before payments are included.\n"
            "2. include_empty     (bool, optional, default=false) Whether to include addresses that haven't received any payments.\n"