Per this article from the Financial Times
https://www.ft.com/content/06a44def-...e-2ca6091e0e1e
The main sticking point is now Russia overflight rights:
The US has offered to grant Chinese airlines the same number of weekly flights between both countries as American carriers — but only if they agree not to fly over Russia, according to six people familiar with the talks.
Moscow banned US carriers from flying over the country after Washington prohibited Russian airlines from flying to the US in the wake of Russia’s full-scale invasion of Ukraine. Chinese airlines are not banned from Russian airspace.
US carriers have 12 weekly flights to China, while Chinese airlines have eight to the US. The American carriers face higher fuel costs than their Chinese rivals whose routes over Russia to the US are much shorter.
US airlines have lobbied the Biden administration not to grant China more flights because of the cost gap. The shorter route over Russia also allows Chinese carriers the advantage of flying directly to the US east coast.
One Chinese embassy official said Beijing’s proposal to equalise weekly flight numbers — to give both sides 12 — was “quite reasonable”. He blamed Washington for the stalemate in the negotiations, saying China did not accept that its carriers should have to avoid flying over Russia.
“The slow progress at the moment is not what we want to see. Frankly speaking, the responsibility lies with the US side,” the official said. “An issue between the US and Russia is not one between the US and China, even less should it be used as a basis for demanding the so-called ‘reciprocity’.”
...
The Chinese official said another reason not to accept the US condition about circumventing Russia was that airlines from other countries, such as India and the UAE, flew over Russia without facing repercussions in the US.
Anyways, CAAC is already planning on reducing US airlines' flights back to 8x weekly (DTW-PVG ends 5/17; DFW-PVG is already back to 2x weekly from 4x). Honestly, I'm surprised CAAC agreed to increase US carriers' flights to 12x weekly (both sides had 8x weekly in 2021 and 2022) before US DOT confirmed that it would reciprocate. I don't think China will make that mistake again.
Also, I doubt China is going to capitulate on the Russia overflight issue, especially since the US is not making the same demand of Middle Eastern and Indian carriers. I would not expect any more direct flights between the US and China until the Russia-Ukraine war is over. Given the desire of hawks in both governments to reduce reliance on each other, the present state probably suits those who are in charge.