Google is placing more importance on whats called RESPONSIVE websites in their search engine results. Older sites, maybe your current live site, were only designed to opened on a desktop computer. These days, websites need to perform well by opening properly on any device be it a normal computer screen, a tablet or one of the many smartphones we all have today. Thats called being RESPONSIVE.
So do you have a responsive website?
More reading here: https://support.google.com/adsense/answer/6196932?hl=en
If you have a minute you can test your website here: https://www.google.com/webmasters/tools/mobile-friendly/?utm_source=wmc-blog&utm_medium=referral&utm_campaign=mobile-friendly
Or contact me.