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.
bool fValidAddress = ExtractDestination(scriptPubKey, address);
        if (destinations.size() && (!fValidAddress || !destinations.count(address)))
            continue;
        UniValue entry(UniValue::VOBJ);
        entry.push_back(Pair("txid", out.tx->GetHash().GetHex()));
        entry.push_back(Pair("vout", out.i));
        if (fValidAddress) {
            entry.push_back(Pair("address", EncodeDestination(address)));
            if (pwallet->mapAddressBook.count(address)) {
                entry.push_back(Pair("account", pwallet->mapAddressBook[address].name));
            }
            if (scriptPubKey.IsPayToScriptHash()) {
                const CScriptID& hash = boost::get<CScriptID>(address);
                CScript redeemScript;
                if (pwallet->GetCScript(hash, redeemScript)) {
                    entry.push_back(Pair("redeemScript", HexStr(redeemScript.begin(), redeemScript.end())));
                }
            }
        }
        entry.push_back(Pair("scriptPubKey", HexStr(scriptPubKey.begin(), scriptPubKey.end())));
        entry.push_back(Pair("amount", ValueFromAmount(out.tx->tx->vout[out.i].nValue)));
        entry.push_back(Pair("confirmations", out.nDepth));
        entry.push_back(Pair("spendable", out.fSpendable));
        entry.push_back(Pair("solvable", out.fSolvable));
        entry.push_back(Pair("safe", out.fSafe));
        results.push_back(entry);
    }
    return results;
}
UniValue fundrawtransaction(const JSONRPCRequest& request)