Please take some time to read the following announcement from Google.
In essence, Google has updated its search algorithm for users doing searches on mobile devices. If your website has ranked well and isnt mobile responsive, you may not be affected too much so as long as your content remains relevant but this could slowly change. Do take the necessary steps to plan this change and shift to a website framework that is mobile friendly.
From NY Times
Talk to me if you need advice to move forward with this change.