Capitol Hill’s six non-voting House delegates for the five U.S. territories and the District of Columbia want their flags flown during military ceremonies in all branches of the armed forces, along with the flags of the 50 states.

But despite support for their cause in the House for two years running, it’s not likely to gain traction in the Senate before the end of the legislative session.

Current practice demands that military bases display all the state flags during official events such as homecomings and award ceremonies. It’s intended as a symbolic gesture of appreciation for the sacrifices of servicemembers.

For members of the military who hail from the District, Guam, the Northern Mariana Islands, the Virgin Islands, American Samoa and Puerto Rico, however, it becomes a gesture of exclusion. Except for those in the Army branch of the military, no military base is required to fly the D.C. and territory flags, or even have them in supply.

“All we want is the recognition,” said Del. Gregorio Kilili Camacho Sablan, D-N. Marianas. “And we want our soldiers and our marines, our coastguardsman, our sailors, to come home, or go on their way to deployment, and see their flag.”

A remedy for this discrepancy has been sought, and endorsed, with little controversy in the House’s versions of the fiscal 2012 and fiscal 2013 defense authorization bills. Rep. Duncan Hunter, R-Calif., offered an amendment containing the language last year, and Sablan was this year’s amendment sponsor.

This language was not included in the Senate’s fiscal 2012 measure, however, and when the two bills were merged in conference the provision was left out.

Now, as the Senate takes up its defense authorization this week, sources familiar with the issue say the provision is not likely to be included this time around either by amendment or during conference.

It’s not entirely clear why the language, seemingly so simple, would not be well received by Senate conferees. Spokesmen for the top Republican and Democrat on the House Armed Services Committee — Reps. Howard “Buck” McKeon, R-Calif., and Adam Smith, D-Wash. — declined to comment and referred inquiries to their Senate counterparts. But press secretaries for Senate Armed Services Chairman Carl Levin, D-Mich., and ranking member John McCain, R-Ariz., did not weigh in either.

Sablan and Del. Donna M.C. Christensen, D-V.I., have been told that senators were concerned about the cost burden for military bases to purchase and fly the additional flags.

“How much could six extra flags cost?” Christensen asked on the House floor Wednesday, as the delegates gathered to speak on behalf of their cause. “It could not even be a fraction of a blip in the defense or the military budget.”

A House Republican aide with the House Armed Services Committee said he hadn’t heard cost to be an issue. He said the provision was not considered a high priority during the conference, and that some senators thought it was not an appropriate issue on which to legislate.

As amendments are offered to the 2013 defense authorization bill on the Senate floor and the bill heads to conference before the year’s end, it’s still possible for a happy ending for the House delegates. The District of Columbia in particular has its share of allies who could take up the cause, including the retiring chairman of the Senate Homeland Security and Governmental Affairs Committee, Joseph I. Lieberman, I-Conn.

Lieberman supports the issue, said his spokeswoman Leslie Phillips. However, she added, “given the time left in the session and the amount of work still needed to be done, it is highly unlikely the senator will have the time to advocate strongly for this.”

Del. Eleanor Holmes Norton, D-D.C., who organized Wednesday’s presentation on the House floor, said she would continue fighting for the proposal’s inclusion in the final bill.

“I would ask the Undersecretary of Defense, I would ask the President of the United States, I would ask the Secretary of Defense, whether there would ever be discretion left to a commander whether to fly the flags of Virginia or Utah or North Carolina or Florida,” Norton said. “That would be considered an insult to those states; we consider it no less.”