As one of the comments says, mosh is great for this sort of thing. I use mosh from my laptop, and it is simply bullet-proof. I can hibernate my laptop, warm it up a few days later, and it's all still connected absolutely fine. Running processes that produce loads of output don't care either. In fact, it's now my preferred way to run long jobs for work that don't want to be interrupted by a dropped connection - the alternative is running them with nohup or "at now".