Despite mutual interest in peace treaty; Israel-Egypt ties threaten to rupture

The first peace agreement between Israel and an Arab state - Egypt - is in trouble.

In the year since the assassination of Egyptian President Anwar Sadat a series of events has drained the agreement of its early vitality. Today there is danger that failure to keep moving forward will result in an irreversible slide backward.

Both Israel and Egypt are very much aware of consequences of any complete rupture. Both have vested interests in avoiding failure.

''I haven't lost faith in peace,'' commented Sadat's successor, President Hosni Mubarak, last week. Israeli Prime Minister Menachem Begin has pointed out that the peace agreement has stood the severe test of the Lebanese war.

Nevertheless, Israelis, distracted for months by the war to the north, are suddenly realizing that relations with their neighbor to the south have become tense and difficult.

The chill first became noticeable with the replacement of Mr. Sadat by Mr. Mubarak. The new President slowed down the pace of normalization in an effort to move Egypt closer to the Arab camp and pointedly refused to visit Jerusalem as Mr. Sadat had done. The announcement Nov. 3 that Mr. Begin was willing to meet Mr. Mubarak in Jerusalem does not appear to break that particular impasse.

The Israeli invasion of Lebanon and its assault on west Beirut further angered and embarrassed the Mubarak government. Egypt responded by virtually freezing trade with Israel, canceling mutual visits planned for official delegations from the two countries, and kept Egyptian tourists from visiting Israel. Most significantly, Egypt's ambassador to Israel was recalled for consultations.

Meanwhile, militant statements began to emerge from Cairo. Last week's statement by Egyptian Defense Minister Abdul-Halim Abu Ghazzala that Egypt and the Arabs had to confront Israel with a deterrent force was a far cry from Mr. Sadat's chant of ''no more war'' during his visit to Jerusalem. And some Egyptian newspapers have returned to the vitriolic attacks on Israel common in pre-peace days.

In this atmosphere, a minor border dispute has taken on new and larger dimensions. It involves an 800-yard stretch of beachfront at Taba in northeastern Sinai and adjacent to the Israeli town of Eilat. When Israel completed its pullback from Sinai last April, it maintained control over Taba until its fate could be settled by negotiation or, failing that, arbitration. Israel, meanwhile, continued to work on a 12-story hotel that had been nearing completion in Taba. When plans were announced last week for its opening in mid-November, Egypt accused Israel of attempting to confront it with a fait accompli and demanded the reopening of the stalled talks on the issue.