Please fill out the following sections to the best of your ability, it will help us investigate bugs if we have this information at the outset. Screenshots are especially helpful, so please provide those if you can.
What platform are you using? It works fine for me on my Apple devices. I checked several plants on your link and found the Plant Phenology Annotation field shown with no data filled in. Looking at the observations through a different view didn’t reveal any annotation values that should have been displayed.
Are you doing Unknown observations? Taxa-specific annotations don’t appear until after the observation is saved with a plant ID. After you submit your ID, then you can switch to the Annotation tab to add phenology. You might have to wait a couple of seconds for the Identify window to refresh.