Your problem was never Penguin

This is the explanation no one wants to hear, but I think it's more common than most of us think. We're obsessed with the confirmed update animals, especially Penguin and Panda, but these are only a few of the hundreds of animals in the Google Zoo.
There were algorithmic link demotions before Penguin, and there are still parts of the algorithm that look for and act on bad links. Given the power that links still hold over ranking, this should come as no surprise. The new Penguin isn't a free pass on all past link-building sins.
In addition, there are still manual actions. These should (hopefully) show up in Google Search Console, but Google will act on bad links manually where it's warranted.
It's also possible that you have a very different algorithmic problem in play or any of a number of technical SEO issues. That diagnostic is well beyond the scope of this blog post, but I'll offer this advice — dig deeper. If you haven't recovered from Penguin, maybe you've got different or bigger problems.