John,
Roberto is correct. If you change the active cell programmatically, the table reverts back to its selection state. This also happens if, while editing a particular cell, the end user clicks on a different cell. You will need to follow Roberto's suggestion, and if you want to prevent users from leaving edit mode, you might have to "swallow" some keypress and left-click events in the table's callback.
Another thing you need to ensure is that the table is the active control. If you have multiple controls in the panel, you might need to stick a SetActiveCtrl call in there somewhere.
As a side note, the next version of CVI will have some feature enhancements to the table control; one of which is the ability to edit a cell automatically, by simply typing on it, eliminating the need to double-click or press .
Luis
NI