Unfortunately there is nothing I'm aware of that allows this to happen with SnagIt itself.
I suppose if you are uploading your captured images to something like ScreenCast.com, you could manually delete images after a certain time period. But there is nothing I'm aware of there that allows you to configure an expiration.
Perhaps if you can expound on the reasoning you would like to see such a feature, someone may have a solution to offer. There are quite a few bright folks that visit here regularly.