It came as no surprise in much of the Arab world that Israeli Defense Minister Ezer Weizman's visit to Cairo failed yesterday to bring about a resumption of Middle East peace negotiations, but the mere fact that the visit occurred while Israeli troops are still in southern Lebanon is evidence of Egypt's determination to work out a settlement.

President Anwar Sadat apparently had little expectation that Weizman would bring any major ideas or proposals that would break the impasse in the negotiations. But Sadat and his top advisers committed themselves in public Saturday, in spite of the Israeli invasion of Lebanon, to try again.

Officials in Syria expressed amazement that Sadat would even receive Weizman under the circumstances. In the Syrian view, Israel's invasion of Lebanon has proved that Sadat's peace initiative was a mistake from the beginning, since the only result has been more Israeli occupation of Arab land.

Despite the failure of the talks, they have renewed Syrian fears that Egypt is drifting toward a separate peace agreement with Israel, which in the view of Syria and the other hard-line Arabs is tantamount to surrender.

After Prime Minister Menachem Begin's return from his talks with President Carter in Washington, Israel made public what it said was a proposed five-point declaration of principles that would serve as the basis for a negotiated peace agreement. But the Israelis admitted that it failed to satisfy even the Americans and therefore would surely fall short of meeting Egyptian terms.

Under the circumstances, Egypt knew there was little prospect for movement and held out little hope that anything was to be gained by resumption of the formal peace negotiations. But Sadat has insisted again and again that he will not and cannot write off his peace initiative altogether.

So last Saturday he called together his National Security Council, Egypt's highest ranking political and military leaders, and they issued a declaration of readiness to go ahead with the talks despite Israel's continued presence in Lebanon. This was in keeping with the Sadat policy of putting the blame for the breakdown of negotiations on Israel.

Sadat likes and repects Weizman, unlike Begin whom he finds fanatical and condescending.

The Egyptians believe that Weizman is a much more realistic and pragmatic negotiator than Begin, and reports from Cairo have indicated that Sadat chose to agree to Weizman's visit because he thinks it possible that Begin may soon be ousted as prime minister and Weizman would replace him.