Mounting evidence that President Carter and the United States lack the power and the will to arrest crumbling of the Western position in the Persian Gulf is converting the Iraqi-Iranian war from an asset to potentially crippling liability for Carter's reelection.

A week ago, shortly after the war broke out, a senior Carter political aide privately remarked that the crisis "is worth five points in the polls" in Carter's nip-and-tuck presidential race with Ronald Reagan. That analysis fits the history and tradition of presidential campaigns; in time of danger abroad, voters tend to rally around their president rather than risk changing horses in midstream.

Political tradition may still hold as Carter enters the October stretch drive. But politicians on both sides are less certain than 10 days ago. A major reason is Carter's apparent inability to bring decisive American influence to bear on the low-grade war or, more importantly, its high-grade implications. t

The first of these is the suddenly degraded prospect of the hostages' returning before the election. Before the war, the prospect was far higher than admitted here; today, it nears the vanishing point.

Other implications of the crisis are staggering. Senior Carter administration officials do not rule out an Arab-backed move against three little islands in the Strait of Hormuz, the choke point in the Persian Gulf, which were seized by the U.S.-backed shah when Iran ruled the Gulf. American strategists believe that would trigger random attacks by Iran's badly depleted air force on Arab Oman, the Arab Gulf emirates and possibly Saudi Arabia.

That would convert the war into an Arab-Iranian conglagration, poisoned by centuries of hostility between the Arabs and ancient Persia. It would force on Carter a more dangerous choice than any he has yet faced: either oppose Arab seizure of the strategic islands, turning the entire Arab world including Egypt against the United States; or support the Arabs, inviting Soviet intervention on the side of Iran. Such a Hobson's choice would publicize American weakness and imperil Carter's political standing.

Sadat's appeal to Carter last week to encourage the overthrow of Ayatollah Khomeini's radical Islamic regime signaled the depth of feeling in the Arab world against Iran. Without tipping his hand ahead of time to the United States, Sadat stunned Carter and the State Department with a proposal that the United States should exploit Iran's military defeat by pressing for an Iranian uprising against the ayatollah.

Given the intimate U.S.-Egyptian connection, Sadat's public plea was seen in Tehran as new evidence of U.S. complicity with the Arabs in the Iraqi invasion of Iran. But in point of fact, after nearly four years in office, Carter's power to influence public statements even by so trusted a friend as Anwar Sadat is negotiable. Within hours of Sadat's statement to Hearst editor John Wallach, the U.S. Embassy in Cairo was privately beseeching him to say no more.

A more ominous signal of Carter's lack of influence with states potentially involved in the Persian Gulf and the surrounding Mideast came from Israel, angering policymakers here. The deputy Israeli defense minister told the respected Israeli newspaper Maariv that Israel could send "substantial aid" to Iran to help it "continue its war against Iraq" if Khomeini were deposed. t

Israel has long been regarded as the closest U.S. Mideast ally. Such a pronoucement from a high Israeli official automatically translates in the Arab world as an order from Washington, raising the immediate -- but ridiculous -- prospect that the United States eyes Israel as an anti-Arab instrument in the Persian Gulf.

"We're close to helpless in this situation," one medium-level American official told us with only mild exaggeration. What seemed late last week to be shaping up as a self-contained miniwar between confident Iraq, bidding for Persian Gulf hegemony, and crumbling Iran, once the pivot of U.S. power, now threatens to impose truly frightening choices on the president.

Given the four-year decline of American will and power, one victim of the Persian Gulf crisis may be Jimmy Carter himself. That would show that the old "don't change horses" rule of presidential elections has no more validity today than America's influence in the world.