The Chinese military mission that was to inaugurate a Sino-American arms relationship did not arrive here this week as the United States had hoped, and no such visit is in sight. In this case, what hasn't happened is viewed with almost as much international interest, and even more speculation, than if it had occurred.

The official reason given by Chinese authorities for not sending Vice Chief of Staff Liu Huaqing to Washington Sept. 16-30 as proposed by the Reagan administration is that more time is needed to prepare for this important visit. However, there have been strong indications over several weeks that this is not the only reason. The most important reason may be Peking's unhappiness over prospective U.S. arms sales to Taiwan.

While expressing hope that no lengthy delay will be involved, administration sources said yesterday that the Liu mission is in limbo at present. It is highly uncertain, the sources said, whether the military mission will be dispatched to Washington before the scheduled late October visit here of Chinese Foreign Minister Huang Hua. Failure to send Liu and his military group before then would suggest that China feels the need for additional high-level political assurances before undertaking an arms relationship.

A well-informed source outside of government said, "The Chinese have made it very plain they are not going to come under these circumstances." The most important of the problems, he said, was the possibility that the Reagan administration will agree to sell a high-performance military aircraft to Taiwan despite strong opposition from Peking.

Taiwan has made clear its belief that Reagan, an old friend of the island bastion, will agree to such an aircraft sale. Top administration officials have denied periodic reports that such a decision has been made, but they have also indicated that new weapons decisions regarding Taiwan are likely to be taken by the end of this year.

Secretary of State Alexander M. Haig Jr., without being more specific, recently said that "there's something on the horizon with respect to Taiwan's defense needs."

Haig, during a trip to Peking last June, made public the Reagan administration's willingness to consider selling China lethal weapons as well as military-related technology and other items on a case-by-case basis.