Suppose:
1) The party with nominal control of the House, Senate and White House takes the blame for a shutdown.
2) The party with nominal control doesn't have a filibuster-proof Senate majority.
It follows that we should see shutdowns during "unified" government because the minority party in the Senate should force shutdowns, and blame the nominal majority. It wouldn't be fair. It is kind of a "stop hitting yourself" thing, but this is politics. Fuck fairness. And yet, this hasn't happened before. Should we be surprised?
Well, when would we have seen this? When was the last time one party controlled everything? 2009-10. Democrats had a brief stint of unified control. Before that, 2001-6, with a brief timeout in the Senate. I'll get to that. Before that, 1993-4. Before that... Carter. Let's get to each of these, in reverse chronological order.
In 2009-10, the Democrats had not only unified control, they had a filibuster-proof majority in the Senate for a time. They started with 58 seats in the Senate, but that was while there was a delay in resolving the Coleman-Franken contest. Groper-Franken didn't get seated for a while. That brought the Dems up to 59. Then, Arlen Specter switched parties, bringing them to 60. Then, Ted Kennedy died, and Scott Brown won a special election to replace him, bringing them back down to 59. Functionally, for any important period, though, the Democrats had either 59 or 60 seats, and it would have been either mathematically impossible, or just insanely hard for Republicans to force a shutdown. They would have needed the likes of Olympia Snowe, Susan Collins, and Scott Brown to go along with it, and that just wasn't happening, even when it was a slim possibility. The numbers weren't on their side. A shutdown in the 2009-10 period of unified government wasn't numerically in the cards.
Before that, 2001-6. Remember I mentioned weirdness? The 2000 election created a tie in the Senate, so Cheney gave the Senate to the GOP with his tie-breaking vote, but Senator Jim Jeffords (R-VT) got pissed off when the party threatened dairy subsidies and such, so he left the party, became an independent, and voted to give control of the chamber to the Democrats, so there was a period of unified government, and a period of divided government. The GOP got full control back in 2002. We really should focus more on the 2003-6 period, then. Why no shutdowns then? Well, you start off with Dubya riding high in the polls in the post-9/11 rally-round-the-flag effect, and the initial positivity of the Iraq War, which started out popular. Don't shut shit down amid that. That brings us to the 2005-6 period. After the 2004 election, the Senate wound up 55-45 Republican (OK, 55-44, with an "Independent" voting with the Democrats...). That would have been enough to shut down the government by filibuster...
A couple of points, though. First, that's a bigger majority than the Republican Party has now. Second, there was another BIG issue in the 2004 Senate elections... judicial filibusters. This led to threats of going nuclear, which led to the Democrats backing down on their filibusters. Third, the Democrats may have been thinking about the 1995-6 shutdowns, which the Republicans "lost"...
Before that, 1993-4. Very different time. The Republicans at the time weren't the party that they are now. If you are looking for a moment in time that turned the Republican Party into the kind of institution that could elect Donald Trump, I'd go with the 1994 election. Why? That was the election that brought Newt Gingrich to power. Gingrich was the leader of the bomb-throwers. Prior to 1994, the GOP hadn't had the majority in the House for 40 years, and a lot of Republicans just kind of accepted that. They figured they should just take whatever deals they could get. Gingrich didn't believe that. He thought that the Republican Party should be as conflictual and destructive as possible in order to win a majority. He had no fucking clue what to do with a majority because contrary to his self-styled image as an intellectual giant, he's a moron, but prior to 1994, he was the primary force opposed to Republicans like Bob Michel, the then-House Minority Leader. The source of the shut-it-down mentality among the GOP is Newt Gingrich, and it didn't become dominant until the 1994 election, which brought him to power. Asking why the GOP didn't shut shit down before Gingrich came to power misses the point entirely.
Yes, I really am saying that if you want to blame one person for the political dysfunction in this country, there's a strong case for Newton Leroy Gingrich.
Anyway, before that... you're back to Carter. We still had Dixiecrats and moderate northeastern Republicans back then.
Really, then, if we are asking why we haven't seen shutdowns during unified government before, we are only asking about that one, weird period during George W. Bush's Presidency. We can probably ignore the 2003-4 period because of the post-9/11 and Iraq War rally effects, and just look at 2005-6. That's it. Two years, and one party. And even then, the Democrats had less of a margin. They had 45 seats rather than 49.
Why haven't we seen shutdowns before during unified government?
You know, thinking through the history, that's kind of a bullshit question.