Answer: Based on your description I am not certain what might be happening to your clematis. There is a possibility it is the start of clematis wilt, as described at the following web page (You may need to cut and paste the complete url into your browser to make it work correctly.)
although since the stems are not turning brown and wilting I suspect it is something else, possibly bacterial, or fungal, such as botrytis. You could also take a look at the clematis diagnostics on the following page (click on the photos for more details)
If none of those seem right, I would suggest you work with your local county extension to get a specific diagnosis of the problem and based on knowing that, decide how to proceed. If a chemical control is needed they will have the most up to date information on what to use and how/when to apply it for best results.
Q&A Library Searching Tips