Did you setup your package to log all errors, warning, etc. If so is there anything in there that would lead you in the right direction?

If that's not a consideration, then run a profiler trace and pull a bunch of perfmon counters and do whatever capturing you can do on the other end while the job runs. It shouldn't take you but a couple days for it to fail again. Also, can your network guys monitor the network while this is going on? It could be dropping connection now and then and killing your package.

Let me know if none of that fixes it.