King Hussein's once brightening hopes for movement in the Arab-Israeli "peace proc as fast as they were building up, with active U.S. encouragement.

As recently as October, the king was at the White House and Ronald Reagan was praising him for "moving steadily and courageously forward" in search of ways to get the Arab negotiations under way. Even congressional skeptics were modestly upbeat about the king's performance on Capitol Hill. Israeli Prime Minister Shimon Peres was publicly praising Hussein for the "vision" he showed in his United Nations speech.

There was a widespread belief that the prickly issues of international "cover" and appropriate Palestinian representation could be worked out in time for Israeli and some joint Jordanian-Palestinian negotiating team to get to the bargaining table by year's end. Now the year is up and it is nearly impossible to find a valid reason why the outlook is so bleak.

The king has not abandoned his efforts, and Jordanian officials are remarkably generous in the credit they give Peres for his good faith. Not so with the United States; the king is putting it about that the Americans have lost interest -- for reasons he cannot fathom.

That's the nub of it: there is no rational or respectable explanation for a diminished U.S. interest. The spoiler in the "peace process" now appears to be nothing more than the vagaries of Ronald Reagan's attention span.

It's true some significant events have occurred since the king's October visit. Even as he was making his case to members of Congress, the Israelis launched an air attack on PLO headquarters in Tunis. But the immediate fear that this would torpedo the "peace process" proved unfounded. Then came the hijacking of the Achille Lauro, with all the diplomated uproar that followed.

There were also the heavy demands of the Geneva summit. Finally, there was a direct U.S.-Jordanian issue involving congressional efforts to shut off U.S. arms sales to King Hussein -- a tug of war that was resolved by putting the question off until March.

But the "peace process" appeared to be weathering all these storms and distractions. According to reliable reports, at the end of October Reagan telephoned Hussein and got the impression that the king was prepared to "swallow" the delay in the arms deal. For his part, Hussein thought he had a commitment from Reagan to take up with Mikhail Gorbachev the question of some sort of international "cover" for Israeli-Jordanian negotiations. Hussein thought he had an agreement, as well, that the Reagan administration would be ready after the summit to give the whole Mideast peace effort a strong nudge forward.

According to some accounts, Riard Murphy, assistant secretary of state for the region, drew up a post- summit plan of action for Secretary of State Shultz. The president was to consider it over his Thanksgiving retreat to the California ranch. But somewhere in the bureaucratic machinery the plan got chewed up.

In any case, Murphy's recent call on the king as something of a bust -- as the Jordanians see it. Murphy arrived more or less empty-handed. He could report nothing much from the summit because, as it turned out, the Mideast "peace process" was scarcely mentioned.

You could argue there were more than enough hard cases to discuss at Geneva. Besides, Shultz's enthusiasm for bringing the Soviets into the Middle East act is said to be minimal. If that's the case, somebody at least ought to tell Hussein roughly where the "peace process" resides on the administration's list of priorities. You can make a case (a bad one, in my view) for a low priority. Or you can make the right case for a consistent follow- through on one of the few foreign policy issues that bear the stamp of a distinctive Reagan initiative.

But there is no case for blowing hot and cold for no good reason -- other than the administration's inability to establish an agenda of serious concerns and to hold to it under the pressure of the inevitable distractions. That is a certain invitation for Hussein to give up on what is, for him, at best a chancy "peace process." It is an incentive as well for him to tend to his kingdom's shaky security by looking for a more dependable source of arms and other support.