The death of Anwar Sadat raises the question of whether the intimate Egyptian-American relationship that he built -- so crucial to both countries' diplomatic strategies -- can survive without its principal architect.

Ironically, the nature of that complex relationship, and its fragility, were illustrated just last weekend when the man who will now succeed Sadat, Vice President Hosni Mubarak, visited Washington to press for speedier deliveries of U.S. arms to Egypt and Sudan.

According to Arab sources, Mubarak was displeased at the cool response to his pleas after his whirlwind round of meetings with President Reagan, Secretary of State Alexander M. Haig Jr., Defense Secretary Caspar w. Weinberger and other senior American officials.

Mubarak's frustration reflects long-standing Egyptian concerns that the United States is doing too little ot protect both U.S. and Egyptian interests in the Middle East. His annoyance may also stem from concerns within the Egyptian military that the United States has never fully compensated for the cutoff of Soviet military aid to Egypt, on which Egypt's officer corps depended until 1973. (Mubarak is a former commander of the Egyptian Air Force.)

Egyptian officers thought Sadat's new relationship with the United States after 1973 "was useful economically to Egypt but not good for the military," according to a senior official in the Carter administration who dealt with Cairo's concerns.

Now that Sadat is dead, the Reagan administration is hastily reconsidering its attitide toward the arms requests Mulbarak made last weekend, according to one senator who spoke to Mubarak when he was here.

The strains over arms supplies are an example of the many difficulties in a relationship of enormous importance to both countries, a relationship produced by one of the historic geopolitical reversals of the modern era.

Just 10 years ago Egypt was still the leading Soviet client in the Middle East, with nearly 20,000 Soviet advisers installed in the Egyptian government and military establishment. Today, as a ranking official in the Carter administration out it, Egypt has become "as close as we've got" to an American client state in the Arab world -- the recipient of more than half of all U.S. foreign economic aid, large amounts of military assistance and more U.S. food aid than any other nation.

But the relationship has gone far beyond aid. In the search for stability in the Middle East, both countries depend totally on the other's good will and cooperation. Since the fall of the shah and the Soviet invasion of Afghanistan, Egypt has become "the pivot, the linchpin of our whole policy" in the Middle East and the Persian Gulf, according to a former American official.

If the so-called Carter Doctrine, reiterated in amodified form by President Reagan last week, has any validity, it depends on Egypt. All U.S. plans for protecting the Persian Gulf from new Soviet incursions assume that American forces will be able to use Egyptian bases, particularly the Egyptian air base at Ras Banas. They also assume total cooperation from the government in Cairo.

Sadat's every statement on the matter suggested that these assumptions were acceptable as far as he was concerned. Indeed, the late Egyptian president made several risky gestures to reinforce his American connection, including training Afghan guerrillas after the Soviet invasion and shipping Soviet-built arms to the rebels in an operation run by the CIA. It was a sign of Sadat's personal confidence in his U.S. connction that he disclosed this covert operation in an American television interview.

Sadat also turned over to U.S. intelligence the most advanced Soviet weapons Egypt had received -- a source of valuable intelligence, according to American sources.

In turn the Americans did special favors for Sadat and Egypt. The two countries agreed to an intimate exchange of intelligence information that has been beneficial to both, according to Americans.

And of course there was more traditional American assistance. Last year Egypt received $1.7 billion in U.S. military and economic aid.

Perhaps the most effective non-military American aid has been food shipped to Egypt under Public Law 840. Both this year and next, this aid is valued at about $338 million, more than any other country will receive.

Economic assistance has been much less effective, according to U.S. sources. A struggling economy is one of the facts of Egyptian life that Mubarak will inherit.

In the military sphere the United States has assumed the task of re-equipping Egyptian forces, but at a pace that some Egyptian officers consider inadequate. After "years of deterioriation" of the arms provided by the Soviets, in the words of former defense secretary Harold Brown, the Egyptians are now receiving American F16 fighter-bombers, M60 tanks, Hawk ground-to-air missiles and other modern equipment. But Egypt has requested much more than the United States has agreed to give or sell, including ships for its navy.

U.S. troops have also provided extensive training for Egyptians.