It is the duty of the correctional facility to prevent prisoners from harming themselves and other inmates. Because Manning is in the early stages of such a long sentence - 35 years, with no release date imminent - it is very possible that depression and hopelessness could lead to future attempts.
When someone attempts suicide, they need help and support. Solitary confinement will only worsen depression and anxiety, which could increase the urge to attempt suicide. Leaving Chelsea Manning alone with her thoughts is not a good idea. She should still have the freedom to be loved, involved, and one with others.
A suicide attempt should not be a punishable offense. People who try to commit suicide need help and compassion. They often feel like they have no hope for the future. Putting them in solitary is about the worst thing that can be done to them at this vulnerable point in their lives.
Chelsea Manning is already in prison for punishment on charges of spying. The attempted suicide may be due to the combination of prison and her transgender situation in a military prison. There should be not be more punishment imposed, instead some medical or psychological assistance to be more compassionate to this person.