The first thing that we would check is whether the soil has become waterlogged. Clematis armandii is very hardy and can usually tolerate cold, but it will suffer if the ground is sodden. If this is the case then you could try moving it to a better drained site or improving the soil by adding sharp grit and plenty of organic matter. It may not survive if the roots have become severely damaged but it is worth a try.
If your plant is suffering from the fungal disease known as Clematis Wilt then it is usually recommended that the stems are cut back to healthy growth, from which new stems should develop. However the problem may recur. Planting clematis deeply can help to combat clematis wilt by encouraging more shoots to develop from below ground. That way, if you have to cut the plant back hard, it will be able to produce healthy new growth from the portion of the stem that is planted below ground - a sort of gardening insurance policy!