Assuming a "normal" beer with healthy yeast with an appropriate amount of priming sugar added, carbonation does not fail. Yeast are pretty good at what they do.
If you don't get carbonation because you forgot to add priming sugar, I've heard of people prying off the caps to add carbonation drops and recapping.
Unhealthy yeast is somewhat improbable because they already fermented a beer (if they were healthy enough for that, they are healthy enough to carbonate).
By "normal" I mean average ABV, etc. I had a stout that had 11-12% ABV to which I added bourbon. This was too high of an ABV to bottle carb, so I force carbed in a keg and used a bottle filler.
As Revvy always says, there are no problems with carbonation - only problems with patience. If you happened to not add enough priming sugar, I'm not sure what to do. It would be tough to say how much extra to use or how to add it.