This answer doesn't deserve its downvote: The problems with tachyons were largely resolved in the 80s, based on work by Stückelberg and Feynman, Schwartz, Recami and others.
The community just lost interest in them because our current models of particle physics prevents bare tachyons:
QFT does predict real tachyonic particles. However, they are solutions of unstable vacua, which transit to a tachyon-free phase via symmetry breaking.
Stringtheory predicted tachyons as well, but got rid of them again when superstringtheory came around.
Tachyons are not gone completely, though: Virtual particles can be off-shell and thus tachyonic and feature in the description of self-energy.
Tachyons can also be useful to explain EPR-type quantum 'paradoxa' without having to give up reality.
The community just lost interest in them because our current models of particle physics prevents bare tachyons:
QFT does predict real tachyonic particles. However, they are solutions of unstable vacua, which transit to a tachyon-free phase via symmetry breaking.
Stringtheory predicted tachyons as well, but got rid of them again when superstringtheory came around.
Tachyons are not gone completely, though: Virtual particles can be off-shell and thus tachyonic and feature in the description of self-energy.
Tachyons can also be useful to explain EPR-type quantum 'paradoxa' without having to give up reality.