Hi Amelia
Interestingly the bounce rate for the page that has dropped is lower than the Homepage. Landing page has a 25% bounce rate while the Homepage is 26.46%.
Average time on page is slightly lower than the Homepage. The only issue here is this was a relatively new landing page and there are older ones that are actually ranking higher with much higher bounce and exit rates. In fact one of the pages that has been ranked #3 for the past month has a bounce rate of over 60%!
The only trend I am noticing is the "time on page" being higher on the landing pages that haven't been effected. I guess this is coming down to a user engagement issue as you suggest. I'll try some more provocative wording to see if that helps although now there will be little to no clicks on the effected landing pages as they have dropped so low!
Thank you for your thoughts
**** UPDATE
After doing a little more comparison it appears that the time on page theory has no weight either as the high ranking pages all have pretty low time on page also... back to the think tank lol.