My child is the same way. She is 3 years old and was prescribed a -2.5 diopter pair of glasses for a -4.0 diopter evaluation. I have not been able to tell of any difference in her vision either. In fact, she used to watch the television from really close but since she got the glasses we don't let her watch as much but also enforce a certain distance; but when now she watches from that distance without the glasses too without any obvious discomfort. I do agree with Torben that they can be hard to diagnose in children just from behavior so I don't know why this is.
On the science though, from what I've gathered so far, in toddlers the muscles controlling the focusing of the eyes become accustomed to focusing close due to near work (or TV / iPads etc) and lack of exposure (outdoor play, sunlight). It is then not possible for this to be fixed unfortunately. In my case, enough of the preconditions were present to convince me that it was our environment that caused her issues.
However, there does not seem to be enough research around this topic. There have been experiments but not enough and not conclusive on how effective treatments are. Some people believe that the glasses in fact have the effect of 'locking' the prescription in place since this is now your eyes' focal point, the muscles have no reason to re-adjust. Apparently, in Asian communities there is a tendency to prescribe slightly less than the measured value for the glasses in order to avoid progression of myopia since the muscles do not relax at the new focal point position. Also, some people think using positive diopter lenses for near work might have the opposite effect. Again, unfortunately, there is not enough research on any of these for anything conclusive.
Finally, I know it's year on from when you asked the question. How is your little one doing now ?