Do you know that the why there is a downfall in the performance of your site? Before assuming that this would be a result in updating of an algorithm check few aspects to be clear on your assumptions. There are many organizations which experience such troubles and thinks for instance that it might be because of a Panda, Penguin or Hummingbird. There are many other reasons why the organic traffic can decrease over time.
At first the changes in the website need to be checked along with the technical issues since the developers regularly do the updates to the website but does not inform SEO team this is also one of the reason to drop the rankings. Site can also lose huge traffic when the URL structures are changes that are not redirected properly. If we consider the current trend desktop search has become stagnant when compared to mobile search engine is growing rapidly but then the majority searches is only from Google.
If the site is not properly optimized for mobile devices then the decline can be seen. If there is a technical error, stale content and lacking of social endorsements or being replaced by the competitors in building out a strong content strategy are some of the reasons down fall of performance and so reviewing historical data will help in speed up your analysis in determining the keywords and pages.
If you have low quality content then you need to worry about penalized by Google for being declined in traffic. And the other thing which people skip is that of tracking code that was not added to the new page templates, in order to build a high quality content based user intent then the tracking code need to be on every page which should have accessible to the search engines.