There's a decent chart of RTG output on figure 2-14 of this paper. From 1985 to 2000, RTG output of Pioneer 10 fell from ~100W to ~62W as the RTGs degraded. (Radioactive material decays, thermocouples degrade, etc, etc.)
Extrapolating this out to 2020 you'd expect an output of ~33W.
Meanwhile, this paper on page D-4 gives a nominal power requirement of ~98W in cruise phase, and, more critically, also gives a power breakdown. Estimated of 98W required, subtract off 24W of experiment power and 2W for the prop heaters, gives ~72W required. Of that, ~28W was to power the TWTA (the amplifier for the transmitter).
So we have the following power estimates:
98W -> everything ok
72W -> no experiments, but everything critical still ok
62W -> power output when Pioneer stopped responding
44W -> power estimate for critical systems without transmitter
Going back to the first paper for a second, note figure 2-19 - the output power of Pioneer 10 dropped drastically over time. This makes sense. The TWTA 'wanted' 28W of power, but likely functioned somewhat with less. Pioneer likely stopped transmitting when the TWTAs undervolted to the point they stopped working altogether.
Unfortunately, even if the TWTAs stopped drawing power altogether - I'm not going to dig into the power system enough to see if the Pioneer's undervoltage protection system would do this - we'd need ~44W to power the critical systems less the transmitter, and we only have 33W.
(This is a little bit unfair. The power system estimates include things like % losses in the inverter and such, which should be scaled.)