I can't say there weren't any during Vietnam because I just don't know, but the numbers that have continued to serve after amputation in the last 8-years has increased each and every year. I think - although I'm no expert - that MUCH of it has to do with the profound advancements in prosthetics.
The DoD generally has also been more receptive to allowing those who wish to stay, so long as they can still function in a reasonable capacity. Some of if is magnanimity on behalf of the DoD, and the rest is probably pure selfishness. Service members are expensive to train, and if you can retain that knowledge from the wounded combat veteran, it adds to the institutional IQ of the DoD.
There have been dozens of amputees in the last several years who have actually returned to the theater of combat, and served in front-line combat billets.
General (Retired) Fred Franks, who commanded the 7th U.S. Corps during the first Gulf War lost his foot while serving as a Major in the 11th Cavalry Regiment. Brigadier General (Retired) Stanley Cherry lost one leg and part of a hand while serving as a cavalry troop commander in Vietnam. They both served full careers.
Amputees were allowed to continue serving provided that they could meet certain physical requirements. Infantry soldiers were usually required to transfer to another branch or specialty in order to continue serving. Today’s prosthetic devices make it a little easier to do, but it still takes a lot of dedication.