No, I don't think bronze goes bad.
Bob Cleek may not be a metallurgist, but he does seem to know what he's talking about. Brazing is probably your best bet. Never trust a forumite's claim to being ignorant. ...or one's claims
not to be ignorant, come to think of it.
Judging from the way the chips break, you probably have a free machining (leaded) bronze. Lead freezes out of the metal as it cools. The little lead inclusions scattered throughout the metal lubricate the cutting tools and break the chips, which is nice for machining, but bad for welding. If you compare the alloy information on a site like
anchorbronze, the weldability of similar alloys, say naval brass and leaded naval brass, is worse for the leaded version.
The art bronze advice sounds good too. My first hit on google was a
question like yours with similar advice and problems. If I needed to, I would have read a lot more.
I don't know what to say about the idea of trying to flow braze metal into the cracks. They are probably fairly well oxidized inside. I think it would be best to cut out the bad metal and braze in a new piece. I have only seen the picture, and I don't know how bad or where the cracking is.