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If I updated my site to comply with mobile, will it effect my ranking of site on search engines as iI heard some people lost rankings when update their sites.
As far as i know it can and it WILL affect your website in positive manner as Google love mobile friendly websites, but also it's user friendly as more and more people using mobiles to browse internet. So having bad affect and loosing rankings is not even possible i guess if these people who say so didn't mess up something badly with their mobile settings.
Actually it would be better because mobile optimization is of utmost importance nowadays. Since many people use mobile devices to look up sites, rather than switching on their computers, it has become imperative for a business to make sure that it has a mobile friendly site. Moreover, Google Search will even be expanding its use of mobile-friendliness as an important ranking sign. There is even a mobile-friendly test tool that allows you to check your site. Basically you can test your pages to see how Google Search sees them, and you can even get a mobile usability report to evaluate how well your site is doing and see what changes and improvements need to be made.
It looks like you are thinking that mobile browsers are not in the same league as computer browsers. Any kind of traffic whether it comes from mobile browsers of computer browsers are all the same. That means your website design that used to be for computer browsers only will get a higher SEO capability when it becomes responsive to mobile browsers. More traffic means a higher ranking in the search engine list.