According to The Planetary Society the Pioneer Anomaly has been solved:
First of all, because the Pioneer spacecraft were spin-stabilized and almost always pointed their big dishes towards Earth. Second of all, because two sources of thermal radiation (heat) were then on the leading side of the spacecraft. The nuclear power sources, more formally Radioisotope Thermoelectric Generators (RTG), emitted heat towards the back side of the dishes. When the dishes reflected or re-radiated this heat, it went in the direction of travel of the spacecraft. Also, the warm electronics box for the spacecraft was on the leading side of the spacecraft, causing more heat to spill that direction. Photon pressure, the same type of thing used in solar sailing, then preferentially pushed against the direction of travel, causing a tiny, but measurable, deceleration of the spacecraft – the Pioneer Anomaly.
Of course this isn’t the first time it has been said to be solved. This isn’t even the first time this theory has surfaced. It’s still interesting regardless. I bet in 20 years scientists will still bet debating.