I've encountered the same problem with a client before. The issue was due to the import of products—thumbnails weren't generated as expected when products were created programmatically.
I strongly encourage you to regenerate your product thumbnails, even if you don't want to.
You can back up the img/p/ directory if you're concerned about any potential regression on your website.
*Dont forget do clear your cache manually after*
Have a great day,
Julien