I've found a couple issues where I should be in input mode with a keyboard, but the keyboard does not appear.
The first instance is when I use Citrix to get at my MS Outlook account. When trying to create a new email or reply to an email, the text box appears but the keyboard will not.
The second instance is when trying to create or reply to a posted message on a college message forum. No keyboard appears.
Kind of maddening.
Searching on the Kindle technical forums, this appears to be a known problem.