On the walking dead , where is military ? You think military builded safe zone ? Just like Wellington on the Telltale ? Also Rick heard helicopter on the Days Gone Bye. And also on season 3 we saw military personel remember governor killed them.
You're right. You'd think if Rick's group is able to figure out how to survive, then the military would be even better at it. I think it depends on if the military is still attempting to operate as a government-controlled unit, or have they started functioning like Rick's group- just a bunch of survivors trying to make it work.
There are actually some examples that even the places were protected by the military were overrun by zombies. As you mentioned, the group was hunted down by The Governor (that time when he rescued a helicopter survivor and later he killed the rest of the man's companions) and the other example being the military who had protected Jenner's lab (and already zombified). Oh, and the military forces who were zombified in Atlanta when Rick first came.
There are many types of trained soldiers, but not every of them would survive well. Anyway, I don't think all of them failed miserably like the ones we've already known. But we can only wait, I guess.