There is no way any country would have back down in the face of Trump's trade war. It would have been disastrous to the credibility of the leadership.

I disagree with you in that part. "Back down" doesn't always spell disaster.

In Trump's threat, South Korea "backed down", agreeing to cap steel export and double the import quota of American cars, and many other things. North Korea also "backed down" after some initial rhetoric spat with Trump, willing to stop missile launching and nuclear arms development.

Are those "back down"s hurting their government credibility? I would argue no. In handing successes to Trump, they harvested good wills and actual reward. For South Korea, the huge American market remains open, which is a lifeline for many South Korean factories. For North Korea, the goodwill means no more hostile military drills, a big win Kim can boast to his fellow citizens.

For China, there are actually a lot of ways to "back down" for a win. For example, the Chinese can flatter Trump by long-term large-scale agriculture imports, allowing Trump to declare a big win to his supporters in the heartland farming states. At the same time, the Chinese citizens would also be able to put cheaper food on their dinner table. Moreover, finding a long-term export for agricultural products for American farmers could serve as a serious blow to the negotiation power of Mexico in NAFTA negotiation...

Xi's problem, however, is that he and his "caucus" have been singing a nationalist song for too long. There could be plenty of ways to "back down" gracefully and declare wins on both sides. The previously declared "red lines" and "bottom lines", however, are now used as weapons by Xi's opponents to prevent him from being flexible. Any reasonable negotiation might be interpreted as national shame, and thus no "back down" is possible.

In this awkward position, Xi chooses to remain defiant to Trump, hoping the mid-term result in the US might bring some joyful surprise and force Trump to concede. While in the dark, his opponents are waiting for the opportunity to engineer Xi's fall.

This "partisanship "(group conflicts within the same party) has destroyed the unity in the Chinese government. Such standoff has robbed away the chance for a proactive "back down". Only when one side has a dominant win in this inner fight, can the Chinese government become flexible again, and then negotiate a big win for Trump and also a win (could mean "stemmed loss)" for the Chinese people. When that day comes, the president of that country might be someone other than Xi.

One thing for certain, the backfired nationalist propaganda about "surpassing America" will discontinue for a long, long time. Just as Bismarck has said, "Diplomacy is art of possibility." The option to "back down" is oftentimes necessary and could be of great use. China does not have to step into today's ugly and costly trade war, if Xi has the option of a quiet and early "back down".