From our records, it looks like this was purchased about 8.5 years ago.
It's very likely that the IR LEDs in the opto-sensors have reached the end of their useful life, as they typically have a much lower lifespan than normal LEDs. It's important to note that when the system is on and power is active, those LEDs are active as well, whether the trackball is being used or not. It may appear that they fail abruptly, but that really isn't the case. They work so long as the output is sufficient, but below that point, there isn't enough output to satisfy the requirements of the receiver, so instead of producing a coherent pulse-train, it's basically putting out information which can no longer be properly decoded, so you get what you are currently seeing.