I\'m training a XOR neural network via back-propagation using stochastic gradient descent. The weights of the neural network are initialized to random values between -0.5 an
Yes, neural networks can get stuck in local minima, depending on the error surface. However this abstract suggests that there are no local minima in the error surface of the XOR problem. However I cannot get to the full text, so I cannot verify what the authors did to proove this and how it applies to your problem.
There also might be other factors leading to this problem. For example if you descend very fast at some steep valley, if you just use a first order gradient descent, you might get to the opposite slope and bounce back and forth all the time. You could try also giving the average change over all weights at each iteration, to test if you realy have a "stuck" network, or rather one, which just has run into a limit cycle.
You should first try fiddling with your parameters (learning rate, momentum if you implemented it etc). If you can make the problem go away, by changing parameters, your algorithm is probably ok.