Reagan was the "Commander in Chief" as are all presidents. VPs are not.
So I would not expect a salute, but I also wonder why the Military is
required to salute a civilian, like the VP?
In her case maybe the salute given by Hitler to the masses is more appropriate. 
A hand salute is a military custom/courtesy. In the past, many presidents were also former military leaders, so they are accustomed to saluting. But, as a civilian, they are not required to return a salute.
It's just a courtesy extended from the lower rank person to the higher rank, and then courteously returned. It doesn't denote subservience or "class".
To be saluted and not render a salute -- or any other acknowledgement of the greeting -- is plain rude and arrogant. Maybe she's just ignorant of the protocol?
She might not be the CinC (yet?), but she has a duty to acknowledge a respectful greeting. She could at a minimum nod or give a simple verbal greeting or "Thank you" to the people keeping her safe.
When standing for the National Anthem, military salute and civilians cover their heart with their right hand. Would it be too much to ask her to cover her heart and say, "Thank you" as she walks past? I guess when you actually care about people, these matters would not even be discussed. She would make an effort to show respect in return in some way. Ignoring them is never the right "optic".