Samsung Galaxy S4 mini — Problem with email syncing when Wi-Fi network identified

I don't think there is any problem down there in fact i guess it is one of the security !!

Even with the wifi symbol showing in the statusbar it doesn't mean it's allowing all network traffic through. With 'open' wifi networks you'll normally need to log in with your email on your browser before you can sync email.

Yes, it may have if you are not connected to the wifi network .... look on our smart devices the first priority is given to the Wi-Fi connection means if you are connected to the Wi-Fi network whether it works or not the device continue to prefer Wi-Fi only, it means if you are connected with a Wi-Fi that is not working (inaccessible) and you are also having an active data connection you are not going to get you're attachments downloaded because you device is giving preference to the Wi-Fi and is asking for the server to response via wi-fi if you are connected with wi-fi network and i guess this is the answer to your question because you were with Wi-Fi, so the device doesn't allow the attachment even you are subscribed with mobile data but if switch that wifi connection off your device will ask the server through mobile network and this time your attachment will be downloaded.. i guess this might be the answer you are trying to get. Let me know if you need more clarification or I didn't understand it i the correct manner !!