Well, it is a tough market even for those of us who are of the more average ability, i.e. not fortunate enough to have went to an elite university.
You must always have what the EMPLOYER wants in mind...what you want comes last. You can have the most perfect academic record, but for whatever reason they may feel you aren't the right 'fit' for them.
So, failing the second stage or whatever, might be because they look for specific personality types: e.g. they might want a leader, or someone assertive or a powerful decision-maker etc. It is hard to fool these sort of tests, so try again in the future or maybe see it as not being the right role and try something else.
Don't be disheartened by it, keep ploughing on.
I read a startling statistic that the top 10 graduate employers will only give job offers to 8 in 1,000 - that's significantly below 1%.
Remember as well that about 80% of people are looking for work in 20% of the market - which may mean you have to be more creative: i.e. identify a problem and apply speculatively.
The downturn may be a blessing in disguise if it enables us to become more creative in surviving such difficult times.