For the second time in a month, barring unexpected action by Congress in the meantime, the District of Columbia and two federal departments will run out of money Monday night when a congressional "continuing resolution" expires.

The failure by one Senate-House conference committee to agree on the proposed downtown convention center continues to hold up the D.C. budget for the 1978 fiscal year.

A similar dispute by another conference committee over federally financed abortions is blocking the budgets of the Labor and the Health, Education and Welfare departments, which are combined in a single appropriation bill.

Funds for D.C. and for Labor-HEW expired when the 1977 fiscal year ended Sept. 30 without new budgets enacted by Congress. Feeling heat from federal workers who faced payless paydays, Congress adopted a continuing resolution Oct. 13 that authorizes spending on a stopgap basis until the end of this month - midnight Monday night.

There are no announced plans in Congress to act on a new continuing resolution. House leaders hope the lack of spending authority will spur the conferees to reach apreements.

The D.C. dispute reflects the determination by two legislator s to hold firm to their differing positions on a loan of $27 million from the U.S. Treasury to pay start-up costs for the proposed convention center. The city government wants to build the facility near Mount Vernon Square NW at a total cost of $110 million.

Rep. William H. Natcher (D-Ky.), chairman of the House District Appropriations Subcommittee, supports the city's request for the funds, which were voted by the House. Sen. Patrick J. Leahy (D-Vt.), chairman of the counterpart Senate subcommittee, opposes granting the funds, which were rejected by the Senate. Leahy also is the conference committee chairman.

Deliberations by the conference committee reached an impasse at its second meeting Oct. 17, with Leahy saying that he was willing to meet again at any time and Natcher not responding publicly.

Yesterday, the two legislators talked by telephone for the first time since Oct. 17, but did not agree when to meet again. Neither would give details of their conversation.

That means that beginning Tuesday the city once again will be without the legal right to spend money, execept for public safety functions. Gladys Mao D.C. deputy budget director, said yesterday that it is the apparent intent Congress that the city should mantain normal operations.

Conferees on the Labor-HEW [WORD ILLEGIBLE] also have deadlocked, and no meetings are scheduled.

Federally financed abortions under the Medicare program is the only issue. The House has voted a near-tou ban on abortions, while the Senator has taken a less restrictive position.

For employees of HEW and Labor the expiration of the continuing resolution raises anew the prospect of payless paydays for 43,000 employee here. Payroll data for midmonth checks must be submitted by Labor to the Treasury by Nov. 9, and by HEW the next day. Unless there is an agreement, or a new continuing resolution no checks can be written.

The American Federation of Government Employees, which represent workers at the two agencies, has tentatively set a lunchtime protest march to Capitol Hill on Nov. 9 if the issue is not resolved by then.