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)
        throw std::runtime_error(
            "listreceivedbyaccount ( minconf include_empty include_watchonly)\n"
            "\nDEPRECATED. List balances by account.\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 accounts that haven't received any payments.\n"
            "3. include_watchonly (bool, optional, default=false) Whether to include watch-only addresses (see 'importaddress').\n"
            "\nResult:\n"
            "[\n"
            "  {\n"
            "    \"involvesWatchonly\" : true,   (bool) Only returned if imported addresses were involved in transaction\n"
            "    \"account\" : \"accountname\",  (string) The account name of the receiving account\n"
            "    \"amount\" : x.xxx,             (numeric) The total amount received by addresses with this account\n"
            "    \"confirmations\" : n,          (numeric) The number of confirmations of the most recent transaction included\n"
            "    \"label\" : \"label\"           (string) A comment for the address/transaction, if any\n"
            "  }\n"
            "  ,...\n"
            "]\n"