Unfortunately, Web-based downloads directly to mobile devices (e.g., smartphones or tablets, including iPads/iPhones) can be a bit of a mixed bag, depending on the particular device and what software the buyer has installed on it -- i.e., there's no way we can force a device to download something from us if it has no such download capability built-in or installed.
Apple iOS devices in particular require the user to have an app already installed that can open the type of file being downloaded -- e.g., downloading a .zip file to an iPad won't work unless the buyer has already installed an app that can open .zip files. Email attachments can be different because they aren't downloading the file via a Web browser, and the email app may have a built-in way to open .zip files which doesn't declare that ability to the OS or other apps on the device.
Part of the reason for that is because iOS has no general-purpose user-accessible storage; each app has its own, dedicated storage allocation, which can only be used to store file types that app can use. Another reason is just Apple being over-protective of their users; they doesn't want users downloading arbitrary files from the Web that they can't use, which could be malicious or just wind up taking up precious storage space if the user doesn't think (or know how) to delete them.
These other discussions here in our forum cover the topic in more detail:
If you expect to have a lot of mobile buyers, you may wish to customize your thank-you/download page with instructions for those buyers in case they have trouble downloading; this help page explains thank-you page customization:
Buyers should normally have no trouble downloading from our system to an actual computer (including laptops and netbooks), and they should be able to sync the file to any mobile device from there, if the device allows it. If your download link works on a regular computer, it should work just as well on any mobile device that's actually capable of downloading from the Web.