I haven't got an iPad and I detest Facebook!
However, clicking on an email link (whether that be on an iPad, Android device or whatever) should open it in the default browser for the relevant device. If you access Facebook via your browser, Facebook's server will try to find a cookie which tells Facebook who you are. If no cookie is found you have to log in.
So I assume that clicking on a Facebook link in your email launches Safari (which is the browser that iPads use by default) but you've managed to configure Safari so as not to save cookies. See 'Enabling cookies using Safari for iOS' here to fix the problem:
http://help.overdrive.com/customer/portal/articles/1481678-how-to-enable-cookies-on-your-mobile-device