A Senate-House conference committee deadlocked yesterday at its second meeting on the District of Columbia's plan for a downtown convention center as neither side gave ground in a two-hour session marked by polite but often barbed debate.

After reaching tentative agreement on nine of the 41 disputed issue in the city's 1978 budget - including continued but curtailed financing for advisory neighborhood commissions - the conferees adjourned without scheduling another meeting. Nobody suggest, however, that deliberations on the proposed $1.3 billion bedget be broken off.

Sen Patrick J. Keahy (D-Vt.), chairman of both the conference committee and the Senate District Appropriations Subcommittee, told reporters: "Right now we seem to be at an impasse."

Leahy stood firm against the $27 million in proposed start-up costs for the $110-million convention center project despite a blunt warning from his House counterpart, Rep.William H. Natcher (D'Ky), that House members are not going to give up the fight for the center.

"On this (House) side, we're not going to recede on it," Natcher said.

If the conference committe cannot reach agreement, the talks would be broken off, with Leahy and Natcher returning to their two houses of Congress for further instructions.

That process has marked the off-again, on-again debates over federally fianaced abortions, in which neither house has been willing to back off from its position. The abortion dispute has stalled enactment of appropriations for the Health, Education and Welfare and Labor departments.

Because their new budgets were not enacted before the 1978 fiscal year began Oct? 1, Labor, HEW and the D.C. government all are operating under terms of a continuing resolution enacted by Congress last Thursday. That resolution will expire Oct. 31.

The House approved U.S. Treasury borrowing for the center by thin margin of 196 to 187. Natcher, who did not manage the Treasury borrowing bill when it came up for that vote, asserted he would have won a more decisive victory had the bill been under his control.

At yesterday's conference, Leahy and Natcher - both former prosecuting atorneys for their home counties - faced each other across a table with a green baize top. At times, it sounded like they were debating District home rule rather than the city budget.

Natcher called Leahy's rejection of the convention center "a direct repudiation as far as home rule is concerned . . . I don't think you should be in that position . . . regardless of how you feel about (the center)."

Leahy replied that Natcher's own insistence led to Congress keeping budgetary control over the District when it voted in 1973 to grant home rule. He contended that Natcher's sub-committee violated home-rule principles in the pending budget by eliminating the entire $1 million sought by the city for continued operation of its 36 advisory neighborhood commissions (ANCs). The Senate recommended a $5000,000 outlay.

Countinued financing for the ANCs was one of the few important items in the city budget agreed upon by the Senate-House conferees yesterday. The commissions will get $400,000, plus the right to spend $150,000 left over from the last fiscal year.

The conferees also agreed:

To provide $449,000 and authorize 23 jobs to carry out a program against child abuse and neglect that was voted on by the city-subsidized fare of 10 cents for each trip. Pupils who live more than 1 1/2 miles from their schools now get free bus tokens.

All the other items agreed upon yesterday were small. Bigger items were discussed and passed over mainly at Natcher's request, apparently because he wanted to keep them as bargaining chips in the debate over the convention center.

These bigger items include such matters as the size of the Police Department, the right of the University of the District of Columbia to start work promptly on its new Mount Vernon Square NW campus and the size of the federal payment that compensates the city for taxes it cannot collect on U.S. owned property. The Senate has approved a federal payment of $276 million and the House, $295.4 million for 1978.

On the police issue, the Senate is supporting the city's proposal to cut manpower by 186 through attrition while the House opposes it, Sen. Lowell P. Weicker (R-Conn.), one of the conferees, said he would support the House position.

Weicker also urged Natcher and Leahy to seek a compromise on the conposition that a way should be sought vention center. Leahy reiterated his during the upcoming congressional recess to get some private investment in the center project.