Woodpecker stores the fields you create as metadata within your Word document. If your document has a ".doc" ending in the file name, that means that it's in the "Word 1997 - 2004" format.
With this older format, Woodpecker won't be able to save your fields as metadata. This means you'll be able to create fields and insert them into your document, but if you were to re-launch Woodpecker your fields wouldn't show up again. You may see a warning message within the add-in itself if you attempt to use it with a document that has a ".doc" file format.
The easy solution to this is to convert your document to the newer ".docx" format. You can do this one of two ways:
Click "File" - "Save as" - select "File format" and choose ".docx".
Click "File" - "Convert document" (Mac) or click "File" - "Info" and click "Convert" next to "Compatibility Mode" (Windows).