Can I download PS3 game updates from my computer instead?

The PS3 supports the configuration of a proxy server in the Network Configuration. It can be any HTTP proxy server. So you could try to run a simple proxy server on your computer, and point the PS3 to it. Then, the proxy should be able to resume the download if the connection breaks, assuming it is setup as a caching proxy server.

Unfortunately, there's no way of doing this for game updates at the moment. You can update your PS3 firmware by downloading it onto a compatible USB stick but at the moment I can't find any official source regarding doing the same for game updates.

Hopefully this is something that will be added - just because your PS3 is not online, it doesn't mean you should be missing out on patches/updates/free DLC/whatever!