Maybe a vascular problem, like verticillium wilt. You have provided no details, so nobody will be able to get at all specific in their replies. And all you will get is educated guesses even if you post a photo. Some plant pathogens even have to be identified using laboratory procedures.

Yep, I know pretty vague but in all seriousness I'm not sure what to say specifically. Poor health in the tree seems isolated to the 2 branches. My neighbor suggested maybe the mulch around it was holding too much water in--fungus?

Moisture-loving species. But mulch shouldn't be on trunk, if it is. Speaking of trunk problems, a friend has a stripebark maple that is failing after many years of growth because it has a girdling root that is pinching it off on one side. You might check for that as well. You might also search www for "maple diseases", "maple dieback" and the like.

Moved the mulch away. There really wasn't that much around the trunk so I don't thing that was it. Talked to another neighbor yesterday--seems that several red maples in the neighborhood died a couple years ago and the three that are left including mine are now experiencing the same thing. So, any suggestions on what I should plant back in the spot because it is apparently on the way down.

You don't know what's wrong with it yet.