Answer
An $H_{3}$ has a third electron which must move into a higher energy state. The ion $H_{3}^{+}$ does not have this third electron and is therefore lower energy with a stable electron configuration.
Work Step by Step
The $H_{3}$ molecule has 3 electrons, only two of which can be in the low-energy 1s state (if they have opposite spins) according to the Pauli exclusion principle. The third electron must be farther from the nucleus, and is less tightly bound, which destabilizes $H_{3}$.
However, $H_{3}^{+}$ has just 2 electrons, both of which can be in the low-energy 1s state (if they have opposite spins) according to the Pauli exclusion principle. This results in a closed shell and a spherically symmetric electron distribution, which is relatively more stable.
