slider revolution stop after loosing tab focus...

Решение - в настройках слайдера - Общие параметры - Дополнительно - След. слайд на Фокус сделать On

I’ve been looking into this for you and it appears to be expected behaviour when you aren’t focused on the browser tab, if you look at revslider/public/assets/js/source/jquery.themepunch.revolution.js line 2462 and onwards. You will see that if you aren’t focused on the browser tab/window, the revslider will stop playing and will resume again when it’s focused.
Try setting “Next slide on focus” to off, in your revslider slider settings.