I inspected the folder.jpg you sent me. It is a perfectly normal jpg image. Resolution is fine at 200x200 and there are no abnormal IPTC or EXIF tags.
I also read the threads you emailed me. They indicate that in late 2006 there was a problem with Windows Media Player 11 and/or Windows Media Center 2005 changing the file attributes of folder.jpg to hidden and/or system. Some users also reported that some of their folder.jpgs had been changed to black images but I didn't see enough corroboration to believe this, and even if true, this is clearly not your problem because the folder.jpg you sent me is fine.
My current theory is that your problem is caused by one of the following:
1) Hidden/System file attributes: It is possible that MC thumbnails do not work when folder.jpb attribute is hidden and/or system. And it is possible that some other program on your system is setting these attributes in the background. This would explain why the thumbnail is present until you play the file. I expect the thumbnail was built correctly when the hidden/system attributes were off. Some time later the attributes were set. Then when you play the track MC rechecks for folder.jpg, does not find it, and your thumbnail disappears.
Please go to the Sinatra folder.jpg using Explorer and right click properties to inspect the Hidden attribute. Is it set?
I don't know a direct way to inspect the System attribute. You can check it indirectly by going into Explorer options and hide system files. Did folder.jpg disappear when you did this?
If either of these attributes are set then I bet this is the problem. We then only need to figure out which app is setting the attribute.
If they are set, suggest you clear them and then inspect once a day or so to see if something sets them again.
To clear Hidden for all files, using Explorer, go to the root folder of your music, right click properties, clear hidden, click apply and then select apply to this folder and all below it.
I do not know how to clear the System attribute. You will have to do some digging to figure out how if System needs to be cleared.
I think we already disabled the Windows Media Player options that might have caused this.
Do you have Windows Media Center on your system?
Your screen shots indicate you might be using an Explorer enhancement or replacement. Is this true?
2) Incorrect MC setting: This is not likely because we have checked everything I can think of except...
Double check your auto-import options. I am talking about the folder specfic option "Ignore special files (folder.jpg, etc.)". I am not certain what this option does, but try reversing whatever it is currently set to. Then run Auto-Import Now.
Have you tried this?