Don't completely rule out your power supply. Is there an abnormal amount of heat building up in it? If it uses semiconductors arranged in a typical full wave bridge setup, you could have a diode problem (just guessing possibly a leaky diode allowing some AC to pass). Sometimes these things can be real buggers to troubleshoot. Finally, if the input is fed from a three phase source (or the output is three phases tied together), you could have lost one of the phases. Stranger things have happened. Let us know what you find. After rereading your post, these are unlikely.
Sorry, but when I reread your post, losing an input or output would most likely cause the voltage AND the current to drop. Higher voltage is really indicative of a higher resistance somewhere in the circuit. If you have an IR heat sensor, you may be able to point it at all your wires and connections and find a hot spot. If you can shut down the system, remove one of the power leads, and take a resistance measurement across the three cells, it should have a resistance somewhere on the order of 0.005 to 0.006 ohms. It will take a somewhat specialized instrument to read accurately down to those levels. When I worked at the power company we had an instrument called a DLRO (Digital Low Resistance Ohmmeter or Digital Low Reading Ohmmeter) for that job. DLRO's usually have 4 leads. Two supply DC at high current (ours ran at 50 amps) and the other two read the voltage drop across the load. Electronics inside the box provided the magical calculations and gave a digital reading in milliohms or microohms.
Something else you could try which would give the same results is with the cells in operation, take a voltage reading across each cell. If all cells read the same, then the problem is most likely common to the cells. If one cell reads higher than the other two by more than 10% I would suspect an issue with the higher voltage cell.