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)
        {
            tallyitem& _item = mapAccountTally[strAccount];
            _item.nAmount += nAmount;
            _item.nConf = std::min(_item.nConf, nConf);
            _item.fIsWatchonly = fIsWatchonly;
        }
        else
        {
            UniValue obj(UniValue::VOBJ);
            if(fIsWatchonly)
                obj.push_back(Pair("involvesWatchonly", true));
            obj.push_back(Pair("address",       EncodeDestination(dest)));
            obj.push_back(Pair("account",       strAccount));
            obj.push_back(Pair("amount",        ValueFromAmount(nAmount)));
            obj.push_back(Pair("confirmations", (nConf == std::numeric_limits<int>::max() ? 0 : nConf)));
            if (!fByAccounts)
                obj.push_back(Pair("label", strAccount));
            UniValue transactions(UniValue::VARR);
            if (it != mapTally.end())
            {
                for (const uint256& _item : (*it).second.txids)
                {
                    transactions.push_back(_item.GetHex());
                }
            }
            obj.push_back(Pair("txids", transactions));
            ret.push_back(obj);
        }
    }