I just found that on my iPad when i click the search icon in header and then click into the text field to enter my search term then the search option dissapear/closes. The same issues at both my websites.
Ok, i have to look into that. But what i can say is that the search form just dissapear when i start typing and the keybord appear in my iPad. BUT if i drag the keyboard to the smaller variant then it works just fine. So it is only the standard bigger keyboard that closes the search form when it appears.
So probably it is only a iPad issue, not with other tablets.