LeRoy Cain, chairman of the mission management team, said the power loss would not affect the spacewalkers' work to attach the robot's hands to its 11-foot arms.
It's too soon to know whether the second spacewalk, also dedicated to robot assembly, will be impacted if the problem persists, Cain said. Power is needed to heat the joints, limbs and all the electronics of the robot, which could be damaged if left cold for days. It's also needed to check out Dextre and get it moving.
"We don't have our hair on fire and need to do something in the next couple of hours, but we're working it," Cain said at a late-afternoon news conference.
NASA's space station program manager, Mike Suffredini, said he was confident the problem was understood and could be resolved fairly quickly.
Canadian engineers suspected the trouble could be with a timer, and were working on a computer software patch to fix it. Other options were being considered, including relaying power to Dextre through the space station's robot arm.
In the worst case, spacewalking astronauts could go back out to disassemble Dextre and leave it in pieces at the space station, Suffredini said. That way, the robot would not have to be heated.
Endeavour's astronauts, meanwhile, got some good news: The object that appeared to strike the shuttle's nose right at liftoff Tuesday, possibly a bird, actually missed the spacecraft altogether. Endeavour's thermal shielding looks to be in good shape for re-entry in two weeks, Mission Control informed them.
Thursday night's spacewalk was the first of five planned during Endeavour's unusually long stay at the space station. Three of them will focus on Dextre.
Dextre -- which cost more than $200 million -- is one of the Canadian Space Agency's main contributions to the space station. It rode up on Endeavour in nine pieces, all of them attached to a transport bed. That transporter, or pallet, was unloaded from the shuttle early Thursday and attached to the railway system on the space station for the Canadian-built robot arm. That's when the power problem struck.
The 3,400-pound robot, when assembled, is 12 feet high and has a shoulder span of nearly 8 feet. It's designed to help spacewalkers with some of their more routine maintenance chores, with the eventual goal of reducing the amount of time astronauts spend outside.
The Japanese storage compartment that also was delivered by Endeavour is the first part of Japan's massive Kibo lab, which means "hope." The main part of the lab won't arrive until May.
It was the first spacewalk for Reisman, who flew up on Endeavour and moved into the space station early Thursday, shortly after the two craft linked up. And it was the fourth spacewalk for Linnehan, who worked on the Hubble Space Telescope in 2002.