Search on mobile devices disappears

I have built our new website using the Housez theme on Wordpress.
Using a mobile device, when people search on the site islandestates.es for any property then go back later to search for another the search facility has disappeared.
I have tried this on 10 different mobiles now and it is the same. I have been communicating with the owner of the theme favethemes, and they tell me the problem is with the cache on the device, to which I replied, All 10 devices!!! and why do I not have the same problem with any competitors search bars just ours.
Can anyone help please, I am pulling my hair out.

If you still need help message me. Your issue seems to be CSS and js related.

Good morning pixelangel, I still have the same problem. I need to purge the cache on the website several times each day to get the search bar to return. I have spoken to the host company, I have pasted what they said:
If this is happening due to the cache, I may suggest two options - either to have the cache disabled completely (the dynamic cache) or to instead ask the people from the theme, which is the exact script or file that they are using for the search option and to exclude it from the caching. The better option may be the second one, as this way only this feature would have the cache disabled for, while the rest of the site keeps being cached, so that it performs well
I asked the theme provider for the information, they have not responded.
Thank you for any help you can give me.