Excellent question... but I am afraid you are not going to like my answer. One of the many freedoms adults in America are afforded is the freedom to determine the course of our mental health care. The only exception (and I am sure you have heard these before) is if a person is overtly a threat to him/herself or will act out aggressively toward another person. In this case, it is possible to have a judge commit the person involuntarily. The courts are the only power that has the right to retain a person against their will.
So, any lengthy hospital stay will have to be of the volition of your brother. If he is beginning to grow neglectful of his biological or hygiene needs (i.e., not feeding himself, not bathing, etc.) then you could pose a stronger argument to a judge; but short of hearing him state explicitly that he is going to hurt himself again, you will not have the necessary leverage.
Now, a final option is to deem your brother as being "incapacitated due to mental illness" and be granted a power of attorney, at which time you would be able to call medical and treatment shots for him. The entirety of this area is a bit outside of my field of expertise, but you may wish to pose the question in the legal portion of Just Answer (i..e, ask about the process and limitation of securing a power of attorney over your brother).
If you are satisfied with the response, please hit "Accept." That is the only way I can receive credit for my answer. Thanks-