Dropdown menu disappears behind slider on Chrome, not z-index issue?

I have a Wordpress site built using the Vamtam Health Center theme, and after upgrading to the latest version, the dropdown menu on my home page disappears behind the slider on Chrome, but not Firefox or Safari. Here's the site:

http://www.morpheusclinic.com

I tried adding the following code, but it doesn't change anything:

#main-menu .menu .sub-menu {
  position: absolute;
  z-index: 999;
}

My web designer is on sick leave, and Vamtam support requires me to disable plugins before they'll look at it, which I can't do because it's a live site. I can't seem to figure this out by myself, so any help would be greatly appreciated!