The saves that use save slots: The folder where they are normally kept is no longer used by your browser. Those are now kept in the folder "#localWithNet", which fortunately is in the same directory as your "localhost" folder. You just have to manually move any old saves from "localhost" to "#localWithNet" and they will work from there. Subsequent saves using save slots will also begin using the correct folder, so you don't have to do this more than once. While I use Firefox to browse, I run games like CoC in Chrome, so this all assumes you use Chrome. I've been told however that the "#localWithNet" folder applies to Firefox as well. Running a search for it in Explorer should work. You can also make a new normal safe in slot 1, then look up "CoC_1" to see where it saves now.
You should also check your browser(s) to ensure they are not set to clear or delete data. For Firefox, for instance, you need to go to "Tools", then "Options", then click on the "Privacy" tab and make sure it says "Firefox will remember history" rather than "Firefox will never remember history". Don't know about Chrome, but it will likely be a similar setting. Programs like CCleaner and the likes also are known to deleting your saves. Make sure that's not doing it.
"Save to File" and "Load from File" issue is still an issue without known solutions. It's likely something specific with CoC itself since other flash games/programs I've tried, including TiTS, don't seem afflicted. Revamp is also stuck with that since it's built around CoC. Either that, or it's on Adobe's end entirely. It's not likely to be fixed unless it's super easy to do and something Kitteh can manage.