Nasa said it wanted to give astronauts more time to repair a machine designed to convert urine into drinking water.
The equipment has failed several times since it was delivered a week ago.
The work came as astronauts started a fourth and final spacewalk to repair a mechanism meant to keep the station's solar panels pointed towards the sun.
Stephen Bowen and Shane Kimbrough are expected to take about six-and-a-half hours to complete the work on two rotary joints in the station's exterior truss.
They plan to install one further new bearing in the joint on the right side of the station, which had become filled with metal filings, and lubricate the joint on the left side to prevent the problem recurring.
The first test of the newly repaired joint will be on Tuesday.
The work has been somewhat slower than expected because Heide Stefanyshyn-Piper lost her tool bag during the first spacewalk.
Unstable centrifuge
Inside the station, ISS commander Mike Fincke is supervising work on the malfunctioning water regeneration system which distils, filters, ionises and oxidises wastewater - including urine - into fresh water.
Earlier this week, the system's centrifuge - needed to separate solid particles from liquid as part of the distillation process - became unbalanced as it spun and shut down before the intended four-hour cycle was complete.
Astronauts removed the centrifuge's rubber dampers on Sunday night and bolted it directly into its rack for increased for increased stability. The repairs made the system work better, but it still shut down early.
They plan to fasten the centrifuge more securely to the rack to further increase stability before running another full four-hour test.
Nasa needs the new system operating before it can expand the station's crew from three to six people, which is currently scheduled for May 2009.
The extended mission means Endeavour's crew will now celebrate Thanksgiving in space and not leave the station until Friday. The shuttle's return to the Kennedy Space Center in Florida is now scheduled for Sunday.
Endeavour's mission is the fourth and final orbiter mission of 2008.
Nasa had hoped to fly a servicing call to the Hubble Space Telescope last month but delayed the mission to May 2009 to prepare for some additional repair work on the observatory.
Nasa plans 10 more shuttle flights before the fleet is retired in 2010.
BBC
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