This appears to be the new Microsoft business model where you rent the software on an annual basis. The idea is that they generate a constant income stream rather than have users buy or be provided with an updated copy every five or so years.
As far as I am aware, the software will continue to work indefinitely with the nag messages as that was part of the deal making it acceptable to commercial users. The only way of preventing update/upgrade messages from appearing appears to involve editing the registry entry of Microsoft Office. This is not for the faint hearted and beyond the scope of this forum. Basically it only involves changing a couple of settings from a 1 to a 0, but if you get anything wrong in the procedure, you could end up rendering your computer inoperable.
Precise details and step by step instructions can be found using the usual search engines.
Disabling updates and upgrades will prevent new security features and updates from being installed and may put you at risk from malware.
So three choices, put up with the nag messages and just delete them when they pop up, pay for the update, or, hack the registry to remove the messages permanently, but potentially expose your computer to a risk of malware infections.