US space agency managers said the ship would not now lift off before 8 May.
It should have left Earth on Friday but has been held on the ground because of an electrical failure in a switchbox connected to a hydraulics power unit.
The youngest of America's reusable spaceplanes is set to deliver a $2bn (£1.2bn) particle physics experiment to the International Space Station (ISS).
On Sunday, Nasa announced the repairs would be lengthy but could not state precisely how long it would take to get the orbiter in a position to make another launch attempt.
"We can tell you pretty much that it's not going to be any earlier than the 8th," explained Mike Moses, the chair of the mission management team.
"That doesn't mean we're going to go launch on the 8th; that just means we know the 8th is our next available opening.
"So we'll kinda start looking at that but we're not ready to set the schedules today. There's still a whole lot of short-term work that has to be done."
Friday's glitch started with an errant heater in one of the three auxiliary power units (APUs) in Endeavour - all of which must be in perfect working order for a launch to be allowed to proceed.
The APUs provide hydraulic power to steer the vehicle during ascent and entry. The heater's job is to prevent hydrazine fuel in a feed pipe to a unit from freezing.
Nasa engineers were not sure at first whether the heater's reluctance to operate was a simple thermostat failure or a more deep-seated issue in an electrical switchbox.Continue reading the main story Endeavour was the last orbiter to be built and flew its maiden voyage on 7 May, 1992It is named after the ship commanded by the British explorer James Cook from 1769 to 1771Total space time to date: 280 days; Total Earth orbits: 4,429; Individual crew members: 133Made the first American ISS construction flight, delivering the Unity ModuleCarried out the mission to correct the Hubble Space Telescope's flawed visionIts radar map of the planet is one of the most used Earth-observation data-sets ever acquiredInspection work inside the orbiter over the weekend has established the problem to be the latter, and managers have decided the whole box, known as load control assembly, must come out and be replaced by a new one.
"There's a heck of a lot of work ahead of the team," said launch director Mike Leinbach. "I'm extremely proud of the work we've already done over the weekend to understand this problem, and now that we've essentially pinpointed the problem to inside of the load control assembly we'll get on with the business of taking that guy out and replacing it with the new one."
Complicating matters is the launch of an Atlas rocket on the nearby Cape Canaveral Air Force Station scheduled for 6 May.
The complex task of switchbox replacement and testing means Endeavour's next opportunity to launch has to wait until after the Atlas has had a chance to get into space.
Managers need then to stage Endeavour's ascent so that the shuttle's movements in orbit do not conflict with a Russian Soyuz vehicle that is supposed to be leaving the space station later this month.
The extra delay means Endeavour's six astronauts have returned to their base at Nasa's Johnson Space Center in Houston, Texas.
The families of the crew were also told there was nothing to keep them at Kennedy.
This included the shuttle commander Mark Kelly's wife - Arizona congresswoman Gabrielle Giffords. She is recovering from a gunshot wound to the head, but was allowed by her doctors to travel to Florida's Space Coast to see her husband's lift-off. She has now returned to the hospital, also in Texas, where she is undergoing rehabilitation.Jonathan.Amos-INTERNET@bbc.co.uk
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