The new U.S. nuclear missile that Soviet President Leonid I. Brezhnev is said to fear the most, the Pershing II, had its second flight test yesterday, and the same thing happened as on its first.

It failed.

Heart of NATO's nuclear modernization program and a center of controversy in the nuclear debate in Europe, the Pershing II is a 1,000-mile-range solid-fueled missile scheduled to be deployed to West Germany just over a year from now. From there it is supposed to be able to hit targets in the Soviet Union within eight minutes.

Yesterday, however, at a New Mexico launching site 100 miles from its target on the White Sands missile test range, the Pershing II did not get off the ground. On its first flight test last July at Cape Canaveral, it exploded 71 seconds after launch.

A slightly embarrassed Pentagon public affairs officer described how the situation unfolded yesterday: "We had a normal countdown. We had missile erection the term for raising the missile to its vertical firing position . We switched from external electric power to internal battery power. And then we got no reading that there was battery power."

With that, just 10 seconds from ignition, the computer running the launch automatically shut down, the spokesman said, and the test was ended. The range safety officer declared a "hang fire," a situation in which for 75 minutes no one was permitted to approach the missile to see what went wrong, in case it fired off on its own.

"This may be just a momentary problem," the Pentagon official said yesterday, "and we could fire it tomorrow."

But, he added, "there is no reason to hurry," and so the test won't take place before next Friday, the next time the range will be available.

The Pershing II is already on a hurry-up schedule of 18 flight tests to meet the NATO decision, made in December, 1979, that would have it available for deployment beginning in December, 1983. That would be the same time that ground-launched cruise missiles are scheduled to start being deployed in England.

NATO agreed to deploy 108 Pershing IIs and 464 cruise missiles to counter the threat from 2,000-mile-range SS20 missiles which the Soviets began deploying in 1979. Late last year, American and Soviet negotiators opened talks in Geneva on these missiles. The U.S. position is that it will not go ahead with its missiles if the Soviets eliminate the 300 or more SS20s they already have deployed.

The Army originally had not expected to deploy the Pershing II until December, 1984, and then not until after it had undergone 28 tests.

Under the hurry-up schedule, the first full-range flight test was supposed to take place last April, and a decision to begin production of the missiles was to be made in June, after at least two tests at the 1,000-mile range.

Designing the new missile turned out to be more complicated than expected. The first flight test was postponed until July, but production of untested missiles began so that some would be available for the proposed deployment date.

The first failure was caused by problems in the first and second stages of the rocket motors, and new motors were built. The Army decided to move to White Sands for yesterday's test and postpone tests at longer ranges until next January.