Eloise died because the "future" event (instruction on how to complete the maze) that was to occur did not take place.
Faraday seemed to wrap up in the results to actually teach Eloise the maze and time expired
Faraday told Desmond that he was "out" for 75 minutes after the Eloise experiment
During the experiment, Faraday says that he will teach Eloise the maze in 1 hour
Failure to complete the events where the conscious traveled to in time causes the death
Eloise could not find a constant because its just a rat, and it died.
Eloise did in fact die of a brain aneurysm. Faraday was right.
Desmond said to Faraday "I know about Eloise". We have since learned that Faraday's mother's name is Eloise. How would Faraday have known which one Desmond was talking aobut?
When talking to somebody, how often do you refer to their mother by their first name? Especially when you've never met them before, "I know about your mother" probably would have been the words said.
Why would someone name a lab rat after their mother? Maybe he gave the rat that name merely in reference to his mother's work with time; however, it is possible that Daniel was angry with his mother when he named the rat "Eloise" because he considers his mother a "rat" of some kind.