Hello again :),
I just got a report back and can confirm, that with the next-to-last version (I never get any e-mails about updates, that is strange, have to pull them manually) input and select fields on any form, be it AJAX search, Gravity forms or hand-made forms, weren’t tappable on mobile at all. In rare cases you could press a bit longer on an input field and finally could enter something.
I just checked for an update and did a manual update to 4.8, and now other forms work well, only the search in the mobile menu still isn’t responding to touches. Do you have any idea if something from your side might be causing this?
All the best