I see the comments from others about working with family or friends being bad. I have done both more than once, and I grew up in a family that was entrepreneurial and supported us through different businesses. Can working with family be hard? Yep. Is it different then working with a stranger? Nope.
Whether you work with family, friends or strangers it is a relationship and so you have to choose wisely who you go into business with. Your brother sounds as though he was lacking motivation before you guys started. My 2 cents is he is more likely depressed than suffering from chronic fatigue, only he really knows right now but either way means he should seek some professional assistance.
In your case, to be direct, you probably picked poorly in this case, not because he is your brother, but because his work focus was poor prior. Continuing to accept it only makes the situation harder, so it does have to be addressed sooner rather than later, which sounds like you are doing.
In my experience and opinion, you need to be direct with him, not confrontational/argumentative but direct. And you need to say that you don't want to continue with him as a co-founder if he can't find the motivation to make things successful. And frankly, ask him if he really wants to be the reason you suffer. No you aren't laying a guilt trip on him because you are prepared to move forward, asking him if he wants to see you fail or the company fail gives him the opportunity to view his actions differently.
The key is you have to make a decision soon. Either you are going to accept him and try to help him through this while he is part of the business, or you cut your business ties and move forward but still help him through this personally to what degree you can. Be clear with this that it is cutting the business ties and nothing else. Make extra efforts for awhile to continue the relationship outside of the business and include him in activities so he feels that not just hears comments. This is the same way you would handle a friend you cut as a co-founder if you value the relationship, which is why I see no difference between friend and family in this case. But you have to make a decision and not blame him for it, it is just facts of the business and move forward. If you spend your time blaming him or delaying the decision you will resent him more everyday and this will destroy the relationship, but if you do that it is your fault not his.