In an order issued on Sunday, the all-Republican court denied a request from a conservative activist and three others, without explaining its decision.
The plaintiffs – a longtime activist Dr Steven Hotze, along with state Representative Steve Toth, US House candidate Wendell Champion, and judicial candidate Sharon Hemphill – had challenged the validity of the drive-thru voting on the grounds that it violated federal law.
In the plea, they had also argued that Democratic Harris County Clerk Chris Hollins exceeded his constitutional authority by permitting drive-thru voting.
“The goal is not ultimately to have (the votes) invalidated. It’s to have them cast right,” Jared Woodfill, a lawyer for Mr Hotze told CNN.
Drive-thru voting is a method of voting whereby completed ballot papers are submitted by placing them in a drop-box. It is an alternative to having voters go in-person to a polling station, vote electronically via an electronic voting system and postal voting.
Granting an exception to in-person voting indoors, Harris County Clerk Chris Hollins had called drive-thru voting a safe alternative during the coronavirus pandemic.
Mr Hollins had argued in court briefs that drive-thru voting follows the same procedures as in-person voting, except that it is done from inside a vehicle after pulling into a tent. He further noted that voters must present photo ID and sign a voting roster before being handed a sanitised voting machine.
Meanwhile, an identical suit from the same petitioners is pending before a federal court and is scheduled for an emergency hearing on Monday in Houston – less than 21 hours before polls open on election day.
“Tomorrow we will be in front of a federal judge who will have an opportunity to review the federal claims we have asserted,” Mr Woodfill, a lawyer for Hotze, told Reuters in an email. He added that his client may eventually take their fight to the US Supreme Court.
US District Judge Andrew Hanen will decide on whether Houston officials illegally allowed drive-thru voting and must disqualify more than 100,000 votes.
The lawsuit is one of the hundreds fueled by the coronavirus pandemic, which has led to challenges over how people can cast their ballots in the showdown between President Trump and Democratic challenger Joe Biden.
The US District Judge will also weigh a request by Democratic organisations and the Senate candidate from the party, MJ Hegar, to join the case defending the drive-thru voting.
The Democrats urged Judge Hanen to reject the suit on the grounds that it was filed two weeks after early voting had begun and four months after Harris County announced plans for drive-thru voting. They further argued that the challenge was filed too late and that stepping in now would create mass confusion and disenfranchise voters whose ballots were legally cast.
Home to 4.7 million people, Democratic-leaning Harris County is the third-largest county in the nation and key to the crucial battleground in Texas where President Donald Trump and his Democratic challenger Joe Biden are bracing for a close election on Tuesday.
Mr Trump won Texas by nine points in 2016 but polls have shown Mr Biden within reach in America’s biggest red state. Democrats need to flip only nine seats to reclaim a majority in the Texas House for the first time in 20 years and have aggressively targeted several races in Harris County.
As of Friday, nearly 127,000 votes had been cast at those drive-thru sites, marking roughly 10 per cent of the votes cast in person during the early voting period.