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() != 1)
        throw std::runtime_error(
            "getaccount \"address\"\n"
            "\nDEPRECATED. Returns the account associated with the given address.\n"
            "\nArguments:\n"
            "1. \"address\"         (string, required) The bitcoin address for account lookup.\n"
            "\nResult:\n"
            "\"accountname\"        (string) the account address\n"
            "\nExamples:\n"
            + HelpExampleCli("getaccount", "\"1D1ZrZNe3JUo7ZycKEYQQiQAWd9y54F4XX\"")
            + HelpExampleRpc("getaccount", "\"1D1ZrZNe3JUo7ZycKEYQQiQAWd9y54F4XX\"")
        );
    LOCK2(cs_main, pwallet->cs_wallet);
    CTxDestination dest = DecodeDestination(request.params[0].get_str());
    if (!IsValidDestination(dest)) {
        throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, "Invalid Bitcoin address");
    }
    std::string strAccount;
    std::map<CTxDestination, CAddressBookData>::iterator mi = pwallet->mapAddressBook.find(dest);
    if (mi != pwallet->mapAddressBook.end() && !(*mi).second.name.empty()) {
        strAccount = (*mi).second.name;
    }
    return strAccount;
}
UniValue getaddressesbyaccount(const JSONRPCRequest& request)