When discussing something unexplainable, we are often speaking of something that has created a mystery. Words like "mysterious" or "mystifying" reflect this meaning. It is also possible that an answer is forthcoming, but it leads to more questions. In this case "cryptic" or "cryptical" might be used. The idiom "deep" can be used to denote information that is being hidden, such as a "deep, dark secret."
Unexplainable may also be used in a case where the answer is there but seems to be just out of reach. In this case "elusive," "baffling" or "tough" would be acceptable. If the answer seems just as confusing as the original question, then you might use "baffling." If the answer is there, but difficult to grasp or understand, then "problematic" would be useful.
If a question does have an explanation, but that explanation revolves around something that you are unable to explain, then "unaccountable" would be appropriate. If the answer is right in front of you but just too difficult to believe, then you would find a simple word like "tough" to be fitting.
If a problem provides an explanation that seems to be refuted by the problem itself, it is said to be self-contradictory. If the answer only appears to be self-contradictory, but may conceal a grain of truth, then "paradoxical" would be appropriate to use.