0.56inch 7segment display failure
Years ago one of my designs once experienced similar unexplained failures- it turned out that the assembly house was using resistor packs marked 470 which were actually 47\$\Omega\$! The excess current caused segment failures, especially in hot industrial environments. Naturally this was also a wake-up call for their inspection and testing. 

Failing the above, I would suggest bad quality displays, but that's fairly rare. 

Edit: If they are failing just as often with 2.2K resistors (and your PCBs are not faulty, clean, dry and uncontaminated) then the displays are faulty, no way around it. Make sure you're getting first quality parts. One possibility is that the internal double-sided PCBs have faulty plated through holes which are cracking at the edges. I've seen that in bare PCBs when the PCB manufacturer has poor control over their process. The display manufacturer (many of which in China are smallish companies) would have known this (high fallout rate) and may have shipped the parts anyway to a customer who demanded the very lowest price (your supplier?). Just a thought.  

Edit2: Since you say you've tried several brands, then we're kind of left with some problem with your PCBs or the environment they are in. LEDs are not very fragile electrically and can withstand a lot of short-term abuse without failure, and your descriptions do not indicate anything remotely dubious electrically.