I don't think there's a grammatical rule, but there is a minor difference in meaning that "a" imparts and vice versa without the "a." Leaving off the "a" makes the phrase more general. This is better if the specific explanation (or whatnot) is not known. Example: "She left the party without explanation." We don't know why she left. It could be she got a call on her phone, or she had to go to work, or she saw someone at the party that she hates. We don't know. "She left the party without an explanation." Here, there is an implication that an explanation was expected, and perhaps that it was rude of her to not explain herself when she left. There is an implication that something specific should have happened (the explanation), but it didn't happen. Example 2: "He ended the speech without warning." Why did he end the speech abruptly? Again, we don't know. There could be many different reasons. "He ended the speech without a warning." Now the meaning is completely different. An expectation is implied, that he should have ended the speech with a warning, but didn't.

It's possible to say "without a reasonable explanation." The confusion is that "explanation" can be a countable or uncountable noun.