You need to do self analysis of possible reasons and try to eliminate them.
At your level,HR of the interviewing companies cannot really play a big role to reject, unless there were any documentary inconsistencies or negative feedback from references or even less than highly positive feedback.
As far as second query is concerned time has lapsed and nothing much can be done now.
People may try to hide mistakes, that is common and HR cannot be exception to a natural human tendency.
Some times perception about an employee can help delay or stop career progress.
Self analysis of your interactions, work relationships needs to be done.Some body may be brilliant in work but necessarily may not be helpful in growth.EQ and personal relationships and how a person is perceived, does play a role.
Do try and find out whether any misstep has been done and correct it.
In work life such situations arise where good officers/leaders are over looked,one needs to draw right lessons from the failure and rectify it by suitable changes in attitudes,interactions etc.
5th November 2018 From India, Pune