It can. 3G is using your wireless carrier's system, so if you don't have a good/strong (any) signal, you can have difficulty downloading.
Unless someone else here knows a better immediate answer, I suggest you try doing the same thing using a WiFi connection instead of your 3G connection.
If the downloads work using WiFi, try it once again using 3G. If you still have trouble via 3G, but not via WiFi, you will know that the problem is with your 3G connection.
If you have the same problem using both 3G _and_ WiFi, then we have to look elsewhere for the problem.