When you visit http://slovnik.cz/ a text box is focused where you can type a word
to lookup.  After submitting a query, that box will be focused again, with the text
inside selected, but conkeror is not in Input-mode.  Hitting tab moves focus to the
"přeložit" button, then hitting S-tab will go back to the input box, and conkeror
will then be correctly in Input-mode.  Alternatively, switching out of and back to
conkeror in the window manager causes conkeror to correctly enter Input-mode for
that text field.

Another interesting "feature" I noticed was that you can't seem to unfocus the box using ESC, it just
regains focus.

slovnik is a frameset page, where the input form is in one frame, and the translation
results are in a different frame.  Therefore when you submit the form, the results
frame navigates to a new page, causing content_buffer_location_change_hook to fire,
which in turn causes conkeror to switch to normal_input_mode.  However, the input
field is still focused in that other frame, so conkeror is left in an inconsistent
state.