Oh, ok. I thought you were talking about the popup itself. The problem on that page is definitely due to responsive behavior, but not something we can control. It looks like the SCLogin module is in a module position which doesn't show on narrow devices.
We can't force the 'Log in' button to show if it's in a module position that gets hidden on your template. The popup that displays after the Login button is clicked is responsive and should show good on a mobile device.
I'd recommend placing the SCLogin module in a different position that doesn't hide, like the social links that also get hidden on a mobile device.
I hope that helps,
Alex