Basically, the spacecraft needs a transponder to communicate with Earth. The transponder is attached to a circuit breaker. For various reasons, the circuit breaker can flip off. When this happens, it sends an "I'm off" status bit to the spacecraft's power control computer, which in turn flips the circuit breaker back on.
The problem is that the transponder circuit breaker, if it switches rapidly, turns itself off without setting the "I'm off" status bit. Since the spacecraft computer doesn't know the transponder circuit breaker is off, it never commands it back on. Consequently, the spacecraft can't send or receive commands and becomes useless.
The paper speculates that one way to break out of this state might be to wait for an eclipse that lasts long enough to drain the onboard batteries, causing the whole spacecraft to lose power. When the spacecraft boots up again after exiting the eclipse restores power, the power control computer will unconditionally command the transponder circuit breaker on, restoring connectivity --- basically, waiting for orbital geometry to turn the whole thing off and on again.
There's more. You might think: "Well, just add a bit of code to the main onboard computer to unconditionally reset the circuit breaker every so often. Hacky, but it works, right?"
Nope. If I'm understanding this right, the power display computer (which doesn't appear to be programmable) is designed to ignore transponder power control commands from the main computer. The paper doesn't explain the reasoning for this resign, but I suspect it's probably to guard against software bugs causing exactly the scenario that the circuit breaker hardware bug caused. So in an attempt to guard against a software bug, the designers lost the ability to work around a hardware bug.
Maybe you could program the software to notice that it hasn't gotten commands for a while and deliberately rotate itself into an orientation that causes a power loss and reset? I'm guessing that the solar panels are arranged in such a way that it wouldn't work, and the attitude control fuel consumption might be excessive.