Most common causes
Occasionally when Word updates itself the "Woodpecker Automation" button can disappear from your ribbon.
The easy way to remedy this is to navigate to the "Insert" tab, click the "My Add-ins" button, click Woodpecker from your list of add-ins, and click "Add" at the bottom of the popup.
Additional causes
If you have Word 2013 or one of the early versions of 2016, the Woodpecker add-in button will not display underneath the "Home" tab as expected. Word 2016 requires build/version 16.0.6769 or later for "Add-in commands" (i.e. the Woodpecker button underneath the "Home" tab) to display correctly. More info here.
If your build/version of Word 2016 is before "build 16.0.6769", please update Word to a later version. Instructions on how to do this are here.