The concession in the contest held on Aug. 7 came after a tally of provisional ballots showed Kobach’s lead increasing.
A citizenship application for 4-year-old Angela Becerra was denied without explanation, her parents say.
In the gubernatorial election, there is still no clear winner between Gov. Jeff Colyer and Secretary of State Kris Kobach.
At least two Kansas counties have reported discrepancies between their tallies and what the secretary of state's office recorded.
The nationally watched contest between Trump-endorsed Kobach and the state’s incumbent governor was too close to call.
The event was to boost the candidacy of GOP candidate Troy Balderson, who is locked in a close race. Trump focused on his achievements and pressed his personal grudges.
The vote Tuesday in suburban Columbus, Ohio, gives the Democrats another chance to make gains in a historically Republican area.
The Kansas Republican is locked in a tight primary race with incumbent Jeff Colyer for governor.
The future of the position was suddenly rendered uncertain after Rep. Joseph Crowley (D-N.Y.) was upset by 28-year-old political newcomer Alexandria Ocasio-Cortez in the June primary election.
The apparent drive-by shooting occurred in Lomas de Chapultepec, an upscale neighborhood in Mexico City, authorities said.