I’ve done testing on this and the only time I see an issue is if I have one set to yes while the other is set to no.
One other thing that can also cause this issue is if you have multiple taxonomy fields on the same post/page for the same taxonomy. You cannot do this and use save terms because each of the taxonomy fields will overwrite whatever was saved by the previous taxonomy field, load terms will then load whatever was saved by the last taxonomy field to be save the last time you updated the post. There is not work around for this.
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