Below is a message from Microsoft Support:
Beginning in June 30, 2017, Project Online will require the latest version of Project to connect to Office 365. We are making architectural changes to features in Project Online which impact older versions of Project, connecting to Project Online. Originally, we communicated this would happen on February 28, 2017, but have extended the deadline to June 30, 2017. We made this change based on customer feedback. How does this affect me? If you are using Project 2016, you need to be on a supported build to connect to Project Online. For Project Professional 2016 customers, the RTM build (16.0.4266.1000) is the minimum build. For Office 365 customers using the Project Online Desktop Client (the subscription version of Project Professional 2016), you need to be on the previous Deferred Channel build (currently build 16.0.6741.2088) or any other build that is more recent. If you are using any prior version of Project, you will encounter issues connecting to Project Online. This change will not affect you if you are not connecting to Project Online.