Done some more looking at your site, and I think it may be related to the pop-up box that you have the count down timer asking for an email sign-up.
I cannot seem to close the pop-up on mobile, so I let the timer run down and then refreshed the page and the problem with the mobile menu went away, so while I cannot be 100% sure that it is the pop-up that is causing the problem, that would be the first thing I would look at.