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() != 0)
        throw std::runtime_error(
            "listaddressgroupings\n"
            "\nLists groups of addresses which have had their common ownership\n"
            "made public by common use as inputs or as the resulting change\n"
            "in past transactions\n"
            "\nResult:\n"
            "[\n"
            "  [\n"
            "    [\n"
            "      \"address\",            (string) The bitcoin address\n"
            "      amount,                 (numeric) The amount in " + CURRENCY_UNIT + "\n"
            "      \"account\"             (string, optional) DEPRECATED. The account\n"
            "    ]\n"
            "    ,...\n"
            "  ]\n"
            "  ,...\n"
            "]\n"