I recently lost a bunch of reputation because two questions I'd offered answers for had been deleted. This seemed to happen very quickly, without their first being closed (I think). I would love to know why the questions were deleted; it might help me to be a better EL&U user! Is there a way that someone of a low-to-middling reputation can find out why a question has been deleted?
There isn't any way for regular users to search for deleted questions. Only mods can do so. High rep users (10K+) can view deleted questions and answers, but only when they already have the link.
You could save all the URLs to the questions you answer in a notepad document, just in case you need them later, or you can ask a mod nicely if they would search for them for you. Of course, that will only matter if you are 10K+, otherwise you won't be able to see the question anyway. But a mod should be able to tell you the closing/deletion details regardless.
Please keep in mind though that the reason only mods can search for deleted questions is to prevent high rep users from engaging in naughty behavior, so don't be surprised if you are expected to have a good reason for wanting to look at a deleted question.
The FAQ says:
Closing is the first step to deletion. The only closed questions that are not deleted are the duplicate questions that are not exact duplicates of another question. In that case, they serve as sign point to other questions, and can help users to find the questions they are looking for.