I have a WAV file that's 91 bars long @ 115 bpm. When I import it into the 404SX it displays the tempo as 122. Plays correctly.

Does the 404SX have a limitation in calculating this?

Surely so. How is your SP-404SX supposed to know how many bars your sample has?
Instead it must assume a common number of bars - like 1, 2, 4, 8, 16, 24, 32, or in this case it seems to assume 96 bars.

96 / 91 * 115 = 121.318681 <- no coincidence

Now I feel dumb for asking. Totally agree with you. Too many unknowns.

The manual talks about adjusting the BPM of a sample in cases where it comes up with half or double the expected value. I wonder if it can compensate for 96/91.

Hehehehehe you can always try

I would chop it in half and then try what you want to do with two samples instead of just one. It'll work that way.