A bit more substance. The American colonies decided to rebel when Britain's fortunes were at an apex.
I'm sure spices and gold are funding this war, but how long can that last? Seriously, I don't know.
Addendum: NL's larger population and greater wealth than Portugal, in gold and sugar, in 'free' land and in its route to Asia, would probably start to create resentment against their little cousins in the motherland. Add in liberal ideas over the next fifty years or so, and you have a recipe for nationalist feeling.
I do plan a breakaway not just yet though. One has to remember that there were differences between the Portuguese Empires and the British and Spanish Empires. Firstly the Portuguese rulers seemed to appreciate the fact that the motherland was resource poor and needed its colonies, allowing for a much freer inter-colonial trade than their British (pre-1800) and especially Spanish counterparts. In addition in OTL there was no distinction between colonial subjects and metropolitan ones. Meaning that Brazilians (Angolans and Goans too) were given important positions in Brazil, the empire and even Portugal itself, becoming judges, governors and filling other high offices. The theory was that they saw the empire as a whole, and officials saw Brazil as one part of a larger empire.
That is not to say that rebellions did not occur. The most notable rebellion in Brazil in OTL was the Inconfidência Mineira in Minas Gerais in 1789, but this was a result of declining gold production in the region that resulted in raising taxes to cover declining revenues to the crown, also it was inspired by the American and French revolutions. In this TL the gold of present-day South Africa has not yet been discovered (only Zimbabwe's), and it is much more abundant that of Brazil's. Keep in mind that people usually rebel during times of economic crisis', during times of prosperity they are generally content with the status quo.
Comparing the Portuguese settler colonies to the British in North America is also comparing two completely different societies. Firstly in the British colonies the settlers were by and large literate, enjoying one of the highest literacy rates in the world, and having a large number of published newspapers and universities, therefore they were more aware of the outside world. In Portugal and its empire this was not the case until perhaps after WW2. Until the University of Lisbon was opened in 1911 there was only one university in the entire Portuguese-speaking world, Coimbra. In 1920 when the Federal University of Rio de Janeiro opened, Brazil finally had a university (granted the military and engineering school dates to 1792). Needless to say neither Portugal nor Brazil were societies of philosophers or great thinkers.
Also in contrast to British North America is the lack of a history parliamentary or participatory institutions of government. The British settlers came from a background that was accustomed to a degree of representation in parliament and local assemblies. In Brazil this was never the case, and I can't imagine it being so in Nova Lusitania. What little representation that did occur was at a local level, creating a very parochial outlook amongst the upper classes only concerned with their vested interests in a region (enslavement of Indians, expulsion of the Jesuits, etc).
What did exist throughout the Portuguese empire was municipal councils called "Senados de Câmara" in each municipality (in Brazil often very large areas). Here "homens bons" literally good men, usually local large landowners, members of the clergy and merchants sat in a city council to preside over matters of local importance. Unlike the cabildos in Spanish America, the senados had a large degree of independent power, especially in remote areas, but again their outlook was very provincial. Larger municipalities sent representatives to the court at Lisbon, to lobby for their interests. It was the senados in the South of Brazil that persuaded the crown to eventually expel the Jesuits.
Also, the senados gave locals in Brazil a degreee of social mobility, for instance in 1740 King João V had been persuaded to order that the names of prominent merchants be included on the electoral roles of one Council, this was followed by the Marquis de Pombal's encouragement of the local business communities to become aldermen.
When a split does occur it is going to be Portugal itself breaking away from the empire as in OTL. I imagine the local bourgeois class in Portugal resenting the competition of wine, olive oil and wool from Nova Lusitania. Also, there will be the crown and the nobility (due to the empire being a source of revenue in governorships and military commands) that is generally suspicious of merchants and lawyers of Lisbon and Porto and thereby supports the colonials. Remember in OTL it was a revolution in Portugal in 1820 that many historians say was Portugal proclaiming its independence from Brazil that caused the split.