Ok ok lets rewind here and look at the evidence before everyone gets stupid, yes?
Alien - no visual account or evidence of the alien eatin of the crew.
Aliens - no evidence of any type of consumption by the alien warriors.
Alien
3 - First visual recording of an alien supposedly 'eating'
Alien Ressurrection - Again, no evidence of the xenomorphs eating.
Now, back to basics people. The alien grows so quickly because it has an extremely fast motabolism, this means it doesn't need foods to mature into full adult hood, what is not known and only specuated is whether or not the aliens actually need food to survive. The filteration tubes on the back of the creature act as a energy filter if you like, taking in all the surrounding gaseous elements and in some cases, liquid elements, these are broken down and fed into the acidic bloodstream and used as fuel for the alien, a truly fascinating biological system in my opinion.
One speculation would be that because the alien in the third film was bred from a dog it was more animalistic in its ways and scavenged like a dog would or a fox, the lack of the dorsal spines could possibly mean the alien had to replenish its resources by other mean - eating. All this is theory but could hold some substance.
As far as how long a xenomorph could go without eating (if it even has to) i would estimate it to be an extremely long period of time, as the creatures can survive in any environmental situation.
www.thorndesigns.netdarkness of acheron