The vine may not be dying because you are touching it- it may have been unhealthy from the get-go. Check to make sure your plant is in good condition: Are there any yellow leaves or stems? Do you see any bugs or fungal spots on it? Are you watering too much or too little? Is the plant getting enough sun? Plants can be delicate, but can usually handle being touched. It's possible that you are being too rough with your clematis, make sure to be gentle and try to let it grow on its own, but I suspect there may be an underlying problem with the plant.