I submitted a paper to an applied-mathematics journal in May 2015, and the first round review took a bit more than seven months. I only received one referee report (there would usually be two), which was generally positive. I submitted the revised draft in mid January 2016, and it is “under review” ever since.
I inquired about the status about four months ago and only got a reply from the journal staff, basically saying that my message has been forwarded to the handling editor (nothing from the handling editor though). I am wondering if it is OK to inquire again? How long should I wait before I make an inquiry on a paper status (without being too pesty).
The journal states that its target processing time from submission to final publication is eight to nine months, and it typically gives reviewers two months.
I inquired the status about 4 months ago and only got a reply from the journal staff, basically saying that my message has been forwarded to the handling editor ...
is telling me that the journal has not forgotten about your manuscript. They are still processing it.
As you are well aware of, reputable math/applied math journals turn around time are very long in general. I have read on this site that two years is not unheard of. Please see this answer for example.
If you are anxious to know the status of your manuscript, I think sending another inquiry is okay since last time you inquired about its status is four months ago. I don't think the inquiry is too pesty. They'll understand.