I'm not sure what you mean by "offline", since our cart should only work in a live Web page uploaded to a server, accessed via a live Internet connection with a regular Web browser at a domain-named page URL. It will not work properly in a local copy of the page on your own hard drive, nor in the "preview" mode of many Web design programs, nor at a URL using a numeric IP rather than a domain name. Pages with cart buttons being displayed in a frame or iframe can also have problems depending on browser settings blocking third-party cookies.
If the cart on your live domain-based site URL is not retaining items added to it, please see the issues explained on this help page (which is for the E-junkie Cart but also applies to FatFreeCart.com carts as well in most regards):
If you're using the FatFreeCart.com service, please bear in mind that we provide that on a strictly do-it-yourself basis with no support whatsoever (that's a major reason it's free :^), so you're expected to figure it out and troubleshoot any issues you may have with that on your own. If you decide to upgrade to the paid E-junkie cart service (aka "FatFreeCart Pro"), that does of course include support with your subscription.