How to stop Endnote omitting the year for some references?
A few options:


It is possible to exclude the year from an in text citation in Endnote. So I'd check that setting. Right clicking the in-text citation should give you a few options.
Make sure you are showing field codes in Word so that you can confirm that you have actually inserted a citation there. Without field codes it's possible that you have written some text manually.
You may want to explore the style settings in Endnote (e.g., go to edit - output styles in Endnote and select the current Endnote style). There are a whole range of settings that you may need to explore. There might be some rules that you can tweak related to how in text citations display.