The most likely method of keeping your connectivity and therefore your visibility, is to rely on services that are standardized. But talking about standardization in the world of EDI is an art form in itself. Still, having all the right pieces in place is a prerequisite. The most basic part of the puzzle is the connection between your internal systems and the service provider. 

Laura Cecere provides a nice roadmap toward attaining visibility and offers a nice 5 step sequence to developing viable and sustainable visibility. Her first step is to "Stabilize ERP Projects." I agree that's the place to start. And truthfully if your internal systems are not rock solid then whatever you connect to/from them are bound to be sketchy at best.

In fact, stability in ERP goes beyond the technical details of making the systems function. Even more important is the need to validate and normalize the data that populates your ERP and subsequently your EDI supply chain interactions. Many companies that have started down the path toward data normalization quickly found that they had multiple version of what they thought was the same data spread across multiple systems ranging from spreadsheets to inventory control systems, to manufacturing and order processing. 

The point of this is that it's more important than it appears from the outside the verify your internal systems even though you've been transacting supply chain orders for years. Start with the connected link between your ERP systems and your supply chain, then move backwards toward the genesis of your data within your company. At the same time work outward toward the end points of your supply chain. It's not likely to be a quick or easy process, but understanding the problems and the individual connections is the only way to make all the pieces work together and to eventually deliver full visibility.