Conservation of energy follows from invariance under translation in time, not inversion. This symmetry states that no matter when you do your experiment, it will give the same results. All isolated systems obey this symmetry (and therefore conserve energy) and no violation of it has ever been detected. (Needless to say, it would be a huge event if it were.)
In classical physics, only continuous symmetries - that is, symmetries that can be continuously connected to the identity transformation - have a corresponding conservation law. Quantum physics does permit conservation laws for discrete symmetries but these laws are far harder to visualize.
An example of this is conservation of parity, $P$, which corresponds to invariance under inversion in space, and which gives the parity - even or odd - of wavefunctions. Temporal inversion, $T$, is even harder to turn into a physical quantity because it requires a full relativistic treatment in which time is a coordinate like space and not a parameter (as it is in non-relativistic quantum mechanics). A third discrete symmetry is charge conjugation, $C$, which exchanges particles for their antiparticles.
It turns out that any consistent field theory must be invariant under all three operations when taken together - i.e. under $CPT$. Thus violation of parity - an experiment and its mirror image behaving differently - is possible, for example, if it comes together with violation of $C$ - i.e. the mirror experiment behaves like the original one if it is made of antimatter -, as was discovered in the sixties.
Violations of $C$ and $P$ together have also been discovered in recent years, which means that in some situations violations of $T$ must occur. The recent $B$-meson experiments confirm this. Since the $T$ symmetry does not correspond to energy but to a far more abstract quantity (which is not conserved), this does not lead to a nonconservation of energy.