This is not a common phrase; I think it's Indian English. I understand it as meaning “the letter is in the process of being issued”, i.e. the decision has been taken to write that letter (a reply to the application, presumably?), and either the content is being written, or it's waiting for someone's signature, or it's in the mail.
Google Books turns up very few occurrences (most of the time, when the two words “under issue” appear next to each other, it's in unrelated constructions like “under issue 42b”. Here are a few citations:
Necessary notification under FERA to give effect to the revised procedure is under issue. [India News]
An Army instruction to this effect is under issue. [Communication from the India Ministry of Defense]
Necessary amendment to Rule 18 (…) is under issue. [India Ministry of Finance memo]