Find My iPhone shows device as 'Offline'
Wow, Big Brother is watching! Contrary to popular belief, the iPhone's cell reception is not perfect, and from time to time you can and will "lose cell," and it will appear offline. This can happen when it enters its energy saving mode when asleep, though you should still receive calls. This can really happen any time you're not within a reasonable line of site to a cell tower, or even when switching between towers, and cell frequencies really don't go through wooded areas or mountains or hills all that well, and by that I mean "not at all." It is completely normal for iPhones and cell phones in general to lose cell connectivity when behind a hill from the nearest cell tower. Also, holding the phone wrong can cause it to lose cell, because just holding it will de-attenuate the antenna. And all cell phones have this feature.

Also, the A-GPS system iPhone uses is also not perfect. GPS itself is far from perfect, and really doesn't work all that well (read "not at all") unless you have a line of sight to 3 or more satellites. The 'A' part of A-GPS means "assisted" and you can read about what that means in the link above, and it mitigates some of the issues with GPS.

Using "Find My iPhone" to track family members is a little extreme. I think a more friendly way to have the same functionality is to use Apple's Find My Friends app. Try to talk Mom into using that instead, and then you can track her at the same time, too, quid pro quo.