Update Jan 26 2017
The deadline has been extended.
Starting in February 2017, Microsoft will no longer support Project 2013 (through Office 365 or MSI) connecting to Project Online. Customers who need to connect to Project Online will need to move to Project 2016. This change is reflected in the Office requirements article.
Please look in the "Client applications" portion in the "Office 365 plans for business, education, and government" section on the Office requirements article<https://products.office.com/en-US/office-system-requirements>.
"Some features in Project Online require connectivity to Project Online Professional, Project Professional 2016, or Project Professional 2013. In February 2017, Project Online client application support will change, coinciding with changes for the Office 2013 version of Office 365 ProPlus:
- Project Online will only support the latest in-market Project client (Project Professional 2016)
- Project Online will only support the latest Project Pro for Office 365 client (currently the 2016 version)"
Update: The latest information on this change can be found here - https://blogs.technet.microsoft.com/projectsupport/2016/12/15/using-project-online-time-to-be-sure-you-upgrade-the-client-software/.