With control of Congress at stake in next month’s midterm elections, Democrats have a rare opportunity to gain a foothold against President Trump’s Republican Party. But if they come up short, it may be in part because of a failure to pursue a key group of voters. It’s a constituency that makes up 13 percent of the voting population, enjoys high voter turnout and is especially concentrated in some decisive swing states. That group is military veterans — and in the battle for their votes, the Democratic Party lags far behind the Republicans.

According to organizers on both sides of the contest, the Democratic National Committee seems to be pursuing a strategy that focuses on running veterans as candidates instead of organizing to reach veteran voters — the D.N.C. tried that approach more than a decade ago, and it didn’t work. In the 2006 midterm elections, Democrats positioned their party as a check against an increasingly unpopular Republican president whose decision to invade Iraq and Afghanistan had worn thin with much of the United States electorate. The D.N.C. established the Veterans and Military Families Council, hoping to drum up support from military members who had seen enough of these wars. No longer, Democrats argued, would their party be pigeonholed as indifferent to the plight of service members. The council coordinated voter outreach in military communities and advanced dozens of veterans as candidates in contentious midterm battles and nicknamed them the “Fighting Dems.”

Democratic opposition to the Bush administration’s wars resonated with voters, who put them in control of Congress for the first time in more than a decade. It was the most sweeping Democratic wave since Watergate, but one of the Democrats’ key missions remained unaccomplished: Only six of the 49 Fighting Dems won their elections. Even though voters had favored Democratic candidates by an average margin of nearly 12 points in opinion polls, the military veterans running as Republican candidates, both challengers and incumbents, collectively saw higher vote shares than the Democrats’ heavily promoted veterans.

Twelve years after the first corps of Fighting Dems was routed, Democrats appear poised for another blue wave. The party is investing millions in organizing what the D.N.C. chairman, Tom Perez, calls “base communities” — a diverse mix of rural whites, ethnic minorities and young people of the sort that vaulted Barack Obama to the presidency in 2008. The D.N.C. is partnering with some new grass-roots organizing groups, and Perez has pledged that the party would build up state-party infrastructures, hire full-time organizers and hold events in churches, on college campuses and in other public spaces in base communities year-round. But this investment does not include any focus on reaching veterans. D.N.C. staffers instead contend that the party’s broader messages will filter into military and veteran voting blocs.