This has happened to me only once, and I thought long and hard of exactly what to do.
I eventually came to this conclusion.
1. Click on 'I don't want to swap'
2. Go to your exchanges and find this swap. Will be at the bottom.
3. Open up swap
4. Click on 'Hide in swap monitor'.
This way, all of your denied swaps are gone into a hidden folder, whereas all your completed and present exchanges are visible.
By going to the bottom of your feedback list of successful swaps, you can find a link that allows you to see all of those 'denied' swaps. I use this to check if I have tried to swap with someone before, but received no response.
Go back to the bottom of the list and the link will remove these 'denied' swaps.
I just double checked the exact condition. Actually it doesn't matter if you update the swap or send messages. It will stop being counted 45 days after the swap was confirmed by both users.