I'm in Zone 4a and the Russian sages did OK through the winter here. We didn't have a lot of snow cover but we did have some for part of the winter. They like to be kept on the dry side so should not need watering every day unless maybe they are in pots. The soil should also be well drained. They tend to flop a bit if not getting enough sun. The only problem I've had with them, and it happens every year, is four-lined plant bugs. They cause the leaves at the ends of the branches to go brown and curl up. They're hard to see, you would need to look closely at the top leaves, preferably early morning when they'r not fully "awake".
If you could post a picture it would help us figure out the problem if none of the above seems to fit. I don't know if daily watering in your soil is enough to cause them to wilt, I rather doubt it unless it is very wet where they are, but always bear in mind that both too little and too much water can cause wilting. Up to a point it can be easier to bring them back from too little rather than too much.