First up, you can develop heartburn reactions to certain foods. I used to love red peppers, now I can only eat them sparingly and with a Tums or two. Soda and carbonated beverages are catalysts for heartburn. If you ate something that was causing mild heartburn, the soda would make it worse, splenda or no splenda.
If I were you, I'd keep a food diary for a week and note when your heartburn occurs. It's possible it could be your body's reaction to the substance. Also possible that you have some acid-reflux. Take that food diary to your doc and have them put the kabosh to it for good!