I drain and clean out my liner ponds every couple years (I used to do it every year, but the physical activity has gotten harder for me), usually in early spring, just before everything wakes up. It's a good time for dividing lotus and lilies, which tend to get over grown, and for tearing out grasses, iris, and other marginals that spread like crazy if not controlled. You can dredge a natural bottom pond, but you need to be careful not to breech the clay containment layer.
Otherwise, oxygen is the main requirement for maintenance. As long as the pond gets enough oxygenation, either from submerged plant material or pumps, then aerobic bacteria will actively clear the water of debris and keep the foul-smelling anaerobes away.
Oh, and most of us have to worry about mosquito control, either with fish or regular additions of BTi.