Repeated attempts to make contact with the pint-sized probe, using NASA's Mars Odyssey craft orbiting the planet and the powerful Jodrell Bank radio telescope in the north of England in the days after 25 December, proved fruitless.
The team that developed Beagle 2, at the Open University in London, began to fear the worst, suspecting it might have fallen into a previously uncharted crater.
Hopes were riding on Wednesday on Mars Express, the European Space Agency orbiter on which Beagle 2 hitched a ride to the red planet.
It is scheduled to try to make contact with Beagle 2 a total of six times through 14 January, with the first attempt set for 12:13 pm (12:13 GMT) on Wednesday.
"We have not in any shape or form given up on Beagle 2," the mission's chief scientist Colin Pillinger said.
The signal the scientists will be listening to is a nine-note ditty, specially written for the little probe by the British rock group Blur.
The saga of Beagle 2 - named after the ship on which Charles Darwin developed his theory of evolution in the 19th century -- coincides with last weekend's successful landing on Mars of the NASA rover Spirit.
Mars Express was due to pass right over Beagle 2 on Wednesday, at an altitude of 375kms.
European Space Agency spokesman Franco Bonacina has said that Mars Express is the last chance to communicate with Beagle 2, which was due to test rock, soil and air samples for signs of past or present life on Mars during a 180-day mission.
He added that if there was no contact, Beagle 2 would have to be classified as lost- and all efforts would then shift towards research using instruments on the Mars Express.
Overshadowed by Beagle 2's travails, Mars Express has enjoyed almost hitch-free progress since its launch from the Baikonur cosmodrome in Kazakhstan on 2 June.