It shouldn't affect the health of your fish, unless your water softener makes your water incredibly soft, and floods your water with Sodium/Potassium. (Which is also bad for house plants and watering your lawn)
I recommend checking out your water softener to see how soft the water actually is. You can also bring a sample of your water to your LPS and ask them to test it there. In my (self-promoted) thread, I talk about the ideal softness for Betta fish: http://www.bettafish.com/showthread.php?t=66595
Bettas can handle "Soft" to "Very Hard". On the testing strips and liquid kits you purchase from stores, they range from "Very Soft" to "Very Hard", so if your water tests in the "Very Soft" zone, then I would be worried.
Some pet stores sell pillows that you throw into a bucket to change the Hardness of your water for you, perhaps you can look/ask for those :)
Best of Luck! I hope your fish gets well soon