I picked up a copy of "The Great Fantasy Adventure Album" (I
think it's put out by Telarc?), which has a LOT of very low-frequency
bass content. When I encode it to AAC, even at a relatively high
bitrate, like 192 or 224 kbps, it seems like a good portion of the low
bass content is being lost.
I know that compression algorithms like MP3 and AAC work by
removing content that the algorithm determines to be less audible than
the rest of the signal, but do they also have an arbitrary low-end
attenuation?

Not that I know of. Low-pass filtering is usually employed (good encoders
allow you to adjust the cutoff) because it's less efficient to encode high
frequencies than low frequencies (related to log f).

Usually, I can't tell the difference between a CD and a 224
kbps AAC file of the same song, but it's noticeable with this one
bass-heavy example.

What are you using for an encoder?