This is based on my observation of several hundred rabbits I have had the pleasure to witness go through training.
All rabbits can succeed at agility but some personality traits will make the training much more difficult. Personality is the prime factor for deciding if a rabbit is a good candidate for training, you need the right mix of activity level and fear factor. A bunny that is very inactive will be difficult to motivate while an over active bunny will be hard to focus on the task at hand. A bun that is very fearful will either freeze in position or run wild which just makes them hard to train, for a bun with this trait the person needs to form a huge trust bond with their bun.
Size is also a major factor for picking out a rabbit that will be good at agility. A very small rabbit may have trouble with high/long jumps while a large rabbit may be prone to injury due to their weight. A size between 4 and 6 pounds usually works the best.
There are always exceptions to the rules, my 2.2 lbs. Netherland Dwarf was consistently able to out jump any bun. Why because she just loved to jump.
Other characteristics may be detrimental to a rabbit's ability to perform well at agility. For instance a very long eared lop may step on his ears while attempting jumps.