There are many factors contributing to neurons dying much faster than other cell types.
This website does not provide original references (for this question, it does for the rest of the article) but sounds trustworthy: http://neuropathology-web.org/chapter2/chapter2aHIE.html
Some factors extracted from here are:
- Aside from small amounts in astrocytes, there is no glycogen storage in the brain.
- Fatty acids cannot cross the blood-brain barrier.
- Lack of a backup energy sources such as creatine phosphate in muscle cells.
Which leave the brain crucially dependent on oxydative phosphorylation, i.e. glucose and oxygen. Additionally of course, neurons are metabolically highly active and use up the small amounts of stored nutrients available at a faster rate than most cells. This is because they need to maintain strong ion gradients across their entire membrane, which spans a larger area than most other cell types due to extensive axonic and dendritic trees; not to mention constantly exocytosing neurotransmitters from the axon's numerous terminals.
Coupled with excitotoxicity as the actual mechanism inducing cell death as explained in the Quora answer linked above (http://www.quora.com/Neuroscience-1/Why-do-neurons-die-so-quickly-when-deprived-of-oxygen), this seems to be a sufficient explanation.