What are the main reasons postdoc applicants get rejected? I'm applying for postdoc jobs right now (math). I was put on the short-list for one position and had an interview but the PI for that postdoc made the offer to someone else. I'm starting to get discouraged and wondering what I'm doing wrong. I showed my research statement to a few faculty members and they said it was fine. I also got a letter from one very well-known mathematician. Maybe I didn't make enough faculty contacts? Was I supposed to have a contact at each place I applied to? Maybe what I am doing is not trendy enough. 

Question 1: What do I have to do to get noticed by the hiring committees? 

Question 2: What are people getting postdocs doing that people who don't get postdocs aren't doing?
There are two big issues: competition and potentially poor fit. Either can knock you out. In some fields, at some times, the competition is fierce. Be happy (a bit) that you made the short list. 

On the other side of the coin, it is possible that a candidate is seen as a poor fit for the position. This is more likely to happen early in the process unless it comes down to personal issues - arrogance, or indifference, or ...

Your materials can be fine and you can be fine, but someone else is just seen to be a better fit at the moment. Soldier on. 

You may not need the rest of the advice, below, since you seem to be able to reach the shortlist, but for others, note that your written materials have to be positive/strong enough to move you from the "all applicants" pile into the "we should look at this person" pile. The second pile is very short and if you don't get into it at a quick reading, you are done. Once you are in the shortlist it becomes more of a personal and less of an institutional "game". If you know you are a marginal fit for a position, don't bother applying except in exceptional circumstances.