Is there any time limit for writing comments on research article? I am from mathematics background, recently I came across an article published in 2009 in which certain classification problem is incomplete and inappropriately addressed, can I write comments on that research article after 7 years ?
Yes, you can publish comments both informally (e.g. on a blog) and formally (by writing a paper that references the 2009 article) irrespective of when the original work was published. Much older articles get referenced and followed up upon.

The only issues to be aware of are:


The authors are somewhat less likely to notice and react to the comments.
Research on the topic may have gone on and your comments may be "old news", or already superseded of their own.