Video files are large, and mobile devices fill up fast. It’s very common for us to troubleshoot for awhile, and then discover the problem is a full device. Check your storage space before you spend too much time troubleshooting.
Another thing that happens fairly often is for a person to start a large video download, which takes a long time via wireless, and then discover the device went into autolock or sleep mode before the download finished. Check your autolock setting to fix this one.
Alternatively, most people watch video streaming rather than downloading. If that's an option for you, that might be a better way to go.
Dropbox
You can also download the file to your device, open it in the iZip app and extract the file to Dropbox where you can watch the video there, and will also have access to the file with your other devices.