When I go to "Duckduckgo" (the search engine) the page appears with no keyboard visible. I let the page fully load. Then I press the text box in the middle of the screen (where you enter queries) to give it focus and make the keyboard appear, and the keyboard appears, the page flickers around a little and then the keyboard closes again immediately. I then press the text box again and this time the keyboard stays up and the cursor is correctly located in the text box. This is repeatable, by simply pressing outside the text box. This closes the keyboard and when I press in the text box next the keyboard appears and vanishes. Pressing another time makes the keyboard stay up, as before.

Interestingly, if I long-press in that box, the problem doesn't occur.