Tachyons accelerate (p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is "transcendent," or infinitely fast. This has profound consequences. For example, let's say that there were electrically charged tachyons. Since they would move faster than the speed of light in the vacuum, they should produce Cherenkov radiation. This would lower their energy, causing them to accelerate more! In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy. Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable.
You can learn more about Tachyons on this site:
http://math.ucr.edu/home/baez/physi...r/tachyons.html