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.
entry.push_back(Pair("category", "receive"));
                }
                entry.push_back(Pair("amount", ValueFromAmount(r.amount)));
                if (pwallet->mapAddressBook.count(r.destination)) {
                    entry.push_back(Pair("label", account));
                }
                entry.push_back(Pair("vout", r.vout));
                if (fLong)
                    WalletTxToJSON(wtx, entry);
                ret.push_back(entry);
            }
        }
    }
}
void AcentryToJSON(const CAccountingEntry& acentry, const std::string& strAccount, UniValue& ret)
{
    bool fAllAccounts = (strAccount == std::string("*"));
    if (fAllAccounts || acentry.strAccount == strAccount)
    {
        UniValue entry(UniValue::VOBJ);
        entry.push_back(Pair("account", acentry.strAccount));
        entry.push_back(Pair("category", "move"));
        entry.push_back(Pair("time", acentry.nTime));
        entry.push_back(Pair("amount", ValueFromAmount(acentry.nCreditDebit)));
        entry.push_back(Pair("otheraccount", acentry.strOtherAccount));
        entry.push_back(Pair("comment", acentry.strComment));
        ret.push_back(entry);
    }
}
UniValue listtransactions(const JSONRPCRequest& request)