Have you tried putting a meter on the xfmr? Try measuring Voltage and Amps on the secondary side, both under load and disconnected from load. This will probably tell you everything you need to know. Also check the line side voltage under both conditions to see if there is any problem there.
Without benefit of these measurements, my first guess is a bad xfmr, unless there is a dimmer on the circuit. They have dimmers made specifically for LV lighting because standard dimmers don't always work properly with transformers, especially electronic transfromers.