1) Isabel was extremely popular, even venerated. Who weren't willing to accept her as empress were the politicians.
2) republicanism never became a popular creed. There was no growth in republicanism in Brazil.
3) slavery abolition caused resentment among coffee planters in Rio de Janeiro, once the most powerful elite in Brazil. By 1889 they had become decadent and had been replaced by the coffe planters from São Paulo, who didn't rely on slaves, but on European immigrants.
4) the Paraguayan War wasn't a bad thing. On the contrary: it rose Brasil's prestige abroad. Brazil built it's own ironclads, eventually becoming the 5th most powerful navy in the world.
Having said all that, the problems were:
1) Pedro II did nothing to defend the monarchy.
2) the government didn't react sooner to increasingly insubordinate army officer corps. Had they punished Deodoro da Fonseca, Benjamim Constant and others earlier, things would have been different.
I think the part about "Pedro II did nothing to defend the monarchy" is the primary point. He pretty much did nothing to fight back even though he remained the most revered figure in Brazil and someone who had the respect of other nations. He probably could have destroyed the coup if he had acted quickly. I've read where after his son died he lost hope and he had no confidence in Isabel (or any daughter) as a female ruler. He went into exile fairly meekly and didn't even complain when the Republican govt. seized his property and didn't keep its word to him. Pedro II knew what was coming and didn't seem to care. The easiest way to keep Brasil an empire was for him to have a different personality.