Bill,
The SA sax plays mono or polyphonically depending on how you play (as it says in the Information on that voice). So if you tend to play in a way (legato?) that invokes mono mode when you're trying to get it to play multi notes (and using LH chords in full keyboard mode will do that), something's gotta give.
I've tried playing as you describe and while it's not a total loss I get intermittent cut outs of not only the RH note, but occasionally the LH too.
You can use the SA BigBandSax which sounds very similar and as far as I can tell doesn't drop out. (It is'nt described as being able to change to mono in the way the above does.)
John