I take it from your example that what you really are asking about is explanations that leave themselves open to questions of the same sort as the original explanation.
It is not, of course, a mistake or fallacy for an explanation to fail to account for its own cause in general. Quite the contrary, the vast majority of explanations are like this.
Q1: Why did Jack and Jill go up the hill?
A1: To fetch a pail of water
In the above, A1 is a perfectly valid explanation that reasonably accounts for the data in Q1. It does not however, explain why Jack and Jill wanted a pail of water, nor does it explain why there was water at the top of the hill (an unusual location for a well), nor would it be expected to.
Explanations always lead to further questions. For example,
Q2: Why do the planets orbit sun in roughly elliptical orbits?
A2: Because that's the shape you get from an orbit controlled by an inverse square force like gravity.
This answer obviously suggests additional questions such as why an inverse square force leads to an elliptical orbit and where gravity comes from. But the existence of follow-on questions does not mean that the original explanation is a mistake; it only means that no answer can answer everything.
However, your two examples were a bit different; each is an example of an answer to a question that leads naturally to another question of the same type as the first one.
Q3a: Where does life on earth come from?
A3: Aliens brought it.
Q3b: Where did the alien life come from?
Q4a: Why is that painting art?
A4: Because it it like other paintings that are considered art.
Q4b: Why are those other paintings art?
However, this is also not, in general, a mistake or fallacy, because there is no reason to expect that an answer to a question about one specific instance would apply to all instances.
Q5a: Why did domino A fall over?
A5a: Because domino B fell over and pushed it.
Q5b: Why did domino B fall over?
A5b: Because domino C fell over an pushed it.
Q5c: Why did domino C fall over?
A5c: Because I pushed it.
In this example, A5a is a correct answer even though it leads to more question. Whether it is a proper answer depends on extra-logical features of language and social interaction. That is, the intention of asking Q5a may not be satisfied by answer A5a, because the person asking the question already knows the answer A5a and is really asking why all of his hard work setting up dominos has come to naught. In such a case, the questioner is really asking:
A5x: Why is my domino setup all fallen over?
A5x: Because Joe pushed over the first domino after I told him not to.
I suspect your dissatisfaction with A3 and A4 is that you think the conversational implicature demands a more comprehensive answer than the one you received. In other words, you thought it was apparent from the conversation that you weren't merely asking Q3a and Q4a; you were asking more generally:
Q3x: What is the ultimate origin of life on earth?
Q4x: What is the ultimate feature that distinguishes art from non-art?
However, in cases like this, your demand for a more comprehensive answer may be unreasonable. The suggestion that life came from aliens, for example is a response to the difficulties of explaining how organic life could arise from non-living chemicals on earth. It is reasonable to speculate that organic life appeared elsewhere where the chemical conditions were more suitable or that there are other kinds of life, not based on organic chemistry, which might be more likely to arise spontaneously (it is reasonable so long as it is only speculation).
In cases like this, a partial answer might be useful and suitable even if it does not answer the ultimate question because it can lead to research opportunities.
In the case of the art example, it is reasonable to suggest that what is considered art today is based on nothing more than the history of art in the past. That is a valuable insight even if it does not answer the detailed historic question of how all art originally attained that status. The person who offers A4 as an answer is providing a literal answer to Q4a and a partial answer to Q4x, which may be perfectly reasonable if the ultimate answer to Q4x is unknowable or is beyond the scope of the conversation.