If it's not your Magento Indexing or Caching, and you're not using an extension or system (like Varnish for caching), that similarly needs to be flushed, it could certainly be your CDN. CDN's like Cloudflare cache components of your site on servers across the globe. In order to do that, they typically store local copies of files, like images on their server network. You should, ideally, be able to flush cache without turning off the CDN completely.
The impact of disabling a CDN mostly has to do with the benefits that you were deriving, and exactly what you're turning off. If you're just turning off caching, the impact will have to do with loading speeds, which may be slower. Your CDN is also taking some of the work off of your main hosting server(s), so you won't have that benefit/protection temporarily.
Your host can probably help you test your CDN, so that you don't have to go it alone.
While I don't want to rule anything out for you, I'd first look at Magento's indexing and caching, and any additional caching, like Varnish. Your web host and/or developer (whoever is patching and maintaining your site for you) should be able to provide more info on what's running in your Magento instance that could be storing this info. They may also have ways of adjusting so that certain things are updated when you save them, if that's something that they believe would work better for you. That depends on the size of your catalog, and other factors.
