5-12mbps is the best you'll see from the network & can be much slower........can still time-out even on a small update.
fwiw; some app updates can be in excess or 30 meg......get a few of those & all won't be downloaded.
I'm sorry that the phone is not updating over the air. We all know the importance of getting the update, and when what you describe happens we recommend using the Software Upgrade Assistant tool.
Follow the steps below and let us know your results.