On what I've tested, it doesn't work in Safari on Iphone 4s and an older Android phone from a friend (don't know which one). On several Iphone 6's it works fine.

Do you know if the iPhone 4s are fully updated? Given their age I'm guessing that Apple hasn't probably updated their software in quite a while, so they'll start seeing problems with a lot of sites.

Yes they are updated, but some of the newest apps don't work anymore on the phones. Is it possible that it has effect on an online website? 

Is there a way to work around this?  Change something in the code, etc so that someone using an older phone can still access the menu?  Do any of the other themes function better with older phones?  The older phones may be outdated, but the reality is, people still use them.  I myself just got an iphone 4 from a friend, my first smart phone, and used it to test out my website's mobile version, and had the same issue.  

I'm not sure if it would be possible without compromising it for other devices. Some of our older, non-responsive themes could possibly work on it, although you wouldn't be able to select it for a site unless you had used one with it in the past.