What can I add to Splenda solution to prevent spoilage?
The easiest and best solution for the problem is to not dissolve it into water in the first place. Powdered sweetener keeps indefinitely. Dissolved sweetener falls smack in the middle of FAT TOM, so you have converted a shelf stable food into an unstable one. 

Assuming that you want to keep it at room temperature, there is not that much you can do. You can reduce the water, but I don't know enough about the solubility of sucralose, it is possible that it is still susceptible to mold at the saturation point, just like sugar. 

You could try acidifying it sufficiently to stop the mold from growing. But then it will taste much less sweet, so you will have to add a much larger amount to your drink, several time the amount you normally use. Alternatively, you can acidify it less and use sodium benzoate as a preservative. It is normally used for industrially produced food, so I cannot suggest the correct ratios of acid to sucralose to sodium benzoate. But note that simply mixing them in any old way won't give you a safe product, you may need industrial recipes for correct usage.