DME has a much longer shelf life than LME. LME contains more water, and with this water a greater water activity value. The greater the water activity, the faster degradation processes can occur, due to the greater availability of reaction substrates. I offer no proof of those reactions are, but carbonyl amine browning, aka Maillard, reactions, seem the most likely culprit.
Many people think that Maillard reactions occur only when you boil the wort, but the fact is they proceed at room temp as well, and their cumulative effects over the course of several months sitting on a shelf can be a noticeable change in taste due to the formation/loss/change of various products in the LME.