According to The Pioneer Missions, my emphasis,
The Pioneer 11 Mission ended on 30 September 1995, when the last transmission from the spacecraft was received. There have been no communications with Pioneer 11 since. The Earth's motion has carried it out of the view of the spacecraft antenna. The spacecraft cannot be maneuvered to point back at the Earth. It is not known whether the spacecraft is still transmitting a signal.
If I am interpreting NASA's depiction of the relative positions of distant spacecraft correctly, it appears that Pioneer 11 is roughly in the plane of the solar system ecliptic:
Given that Pioneer 11 was launched (presumably on a heliocentric orbit) directly toward Jupiter, and assuming for a moment that we didn't deliberately tell it to aim its antenna away from Earth, I don't understand why the Earth's motion would have carried it out of the view of the spacecraft's antenna. Even if the Earth's revolution around the Sun would periodically degrade the signal received, possibly to the point of providing insufficient signal-to-noise ratio to decode the signal, it would seem like the signal strength should peak once a year, with an additional lower peak once a year.
Hobbes' claim of a 0.7 AU beamwidth at Earth even for Voyager (based on -3 dB received power and a 0.32° beam angle (from center to half power)), and wider for Pioneer, would seem to be plenty wide enough that precise aiming would not be required; being in the general ballpark should be enough to be able to establish communications with the spacecraft at least once a year.
We do of course have good reason to believe that the transmitter is no longer working (also here), but that is not what NASA claims in the quote at the top of this question.
What is the basis for NASA's statement that the Earth's motion has carried Earth out of the view of Pioneer 11's antenna?