In part the problem arises from the interface between systems. If you walk into any normal hospital internal medicine floor you'll see about 5 different systems in use, with varying levels of interoperability: the VA, operating what is the largest network of healthcare centers in the country, takes that issue to the next order of magnitude. A lot of paper gets generated at these interfaces. Although the core VA EMR system is solid, there are multiple other systems laid atop it. The VA is attempting to address both the software and processes issue (people outside healthcare don't know this, but the VA is the place to take your career if you wish to do healthcare services research - they're, collectively, the single most innovative group of providers in the country).

The main problem lies with the paper backlog of attempting to get people into the system. I'm personally not aware of how/why military personnel's medical records don't transition directly into the VA, but what happens in practice is a gap between military med. and the VA, where vets find themselves forced to file claims. I suspect that this is in large part because the set of "Vets" and the set of people qualifying for VA care, while overlapping, are not the same (that assertion comes from anecdote: I had an ex in the military, and when she finished her tours I recall that she was not qualifying for VA care because she hadn't been disabled nor gone career, as she explained it). While it's fair to ask why this process is done on paper, it's worth-while to note that prior to just the last handful of years the portion of health records that had been digitized was nearly nil (up until about 5 years ago it was standard practice in most hospitals and private clinics to go digital-to-paper-to-digital). Essentially everyone's records were on paper, and all record transfers happened via fax (and still do, if a receiving physician is not inside the same hospital system on the same EMR as the referring physician).

source: work in hospital QI. I haven't worked in the VA, personally, so I am relating a lot of stuff second-hand, but the boundary between most hospitals' QI staff, the IHI, and the VA tends to be pretty porous, if you're in a healthcare capitol city - so I've heard a lot about the VA from co-workers that have worked there, or are currently engaged in ops research there.