Sounds likely probably bad luck or bad interview skills. You have a plan for addressing the interview skills, but you might also want to consider background issues. You didn't mention any, so I assume there are no criminal records or arrests in your past. However, is it possible that someone you listed as a reference or a previous employer said something negative?
- Make SURE that your references will give a glowing, enthusiastic report. A somewhat reluctant reference who you cornered into doing it will not help much. Select your refs carefully.
- Previous employers. If you think you might get a less-than-stellar report from an employer, perhaps you can mend the fences with them over coffee or beer. Another option is to list a person at the company who would be more positive about you as opposed to your actual boss.
- Are your reference letters written well, with correct grammar and spelling? An airline will not be impressed by a letter written by a 20-something slacker CFI who has no writing skills and doesn't know where the spell-check feature is found in MS Word.
- Are your references appropriate? Your CFI buddies and frat brothers probably don't cut it. You generally want at least one "character" reference from someone held in high esteem by society...professor, military CO, DPE, airline CA etc. You also want two letters from pilots who you have flown with...these should ideally have been your supervisors, not your buddies, unless they have impressive qualifications.
Just some thoughts to cover all bases.