Hey tj11,
After building a demo app it seems like this is a bug where if you switch selected row and then go back to the one you edited it will update the button. However, if you stay on the current row the split button doesn't re-evaluate.
You can work around this behavior by selecting a different row on the table or clearing selection on success.
@Tess this seems like a bug and it would be useful if we could Reset/Clear value of split button component as the only options available are Set Hidden/Set Disabled/Scroll into View.