With Europe's sanctions against Argentina due to expire at midnight Monday, foreign ministers of the European Community failed tonight for the second time in a week to reach agreement on extending the month-old ban on Argentine imports.

Three of Britain's nine European partners--Italy, Denmark and Ireland--were reported still to be resisting continuation of the ban.

In addition, Britain found relations with its community allies sharply strained by renewed strife over a budget issue--a development that did not help London in its call for allied help in the Falklands conflict.

Britain has been demanding a cut in its payments to the community, and, as a negotiating lever, has vetoed increases in agricultural prices wanted by the other nine member nations.

British officials rejected suggestions that other members were trying to pressure London into a budget settlement by delaying action on the sanctions against Argentina, but European officials in recent days have sounded upset by what they said has been a lack of a reciprocal demonstration of solidarity from Britain.

If the sanctions are allowed to lapse, Britain's negotiating position in the Falklands conflict could be weakened seriously. But British Foreign Secretary Francis Pym sounded understanding about the desire of some of his European colleagues to put off a final decision until the last minute.

Pym told reporters that the European ministers had asked for a day's postponement to talk to their capitals again and review alternatives. He asserted, however, that "we need to take that decision" on renewing sanctions "and I expect we will."

Another ministerial meeting was scheduled for Monday evening, which will follow a planned session during the day of foreign ministers of the 15-member North Atlantic Treaty Organization.

Earlier today, Pym met with Secretary of State Alexander M. Haig Jr. for a review of the Falklands crisis. Afterward, the British foreign secretary said negotiations to end the dispute were in a very critical phase and still were "very much alive." He reaffirmed Britains's determination to keep military and economic pressure on Argentina while pursuing a diplomatic settlement.