This isn't anything new, and is a huge problem most businesses offering a freemium model face. Before ditching your free plan you should (obviously) evaluate for yourself what is bringing in the money. If there are little to no upgrades from free to paid then there is a good chance you are not distinguishing the two enough, not offering enough added value on the paid plan, not doing a good enough job driving your free users to the paid plan, or that you need to limit the free plan in a different way.
You can also stop offering a free plan and use a paid trial at a reduced cost or even $1, or just offer a no hassle 30/60 day money back guarantee.
