In James T. Patterson's "Grand Expectations" i read that Eisenhower did not vote (at least in presidential elections) during his career. The book doesn't explain this, but the implication is that, as his duty was to follow the orders of whichever president might be elected, he should refrain from taking sides one way or the other. Was this a common practice for US military officers? Is it still?
Military officer's are traditionally not 'supposed' to hold strong political feelings or at least express them, though this is not necessarily the case as well be briefly discussed below. Roy Boehm, the former commander of SEAL Team Two during the Vietnam era, once expressed to John F. Kennedy 'I didn't vote for ya, but I'd die for ya!' which I think more or less sums up the perspective that most US military officers hold and are expected to hold. There isn't really an expressed 'tradition' of not voting necessarily, simply not expressing strong political views and certainly not campaigning for anyone.
However, the DoD does officially encourage all members of the armed forces to hold opinions, register to vote and do so, as well as engage in political discussion so long as they do not do so claiming to represent the armed forces. Below is my source for this.
http://www.dod.mil/dodgc/defense_ethics/ethics_regulation/1344-10.html