It became popular probably by the time the Turks were expelled, early XIX century. By then the rebels, and then the princedom they founded, created a regular army, and every unit had a trumpeteer, mostly as a signal guy, and it took from there.
Nowadays the brass bands, equally gypsy and native serbian (and both playing the same music) are rather popular, specially at weddings, doček or farewell parties. At the weddings, though, they play only on the street, when the wedding party is entering or leaving the church or city hall; they can't really play all night and their music is strictly instrumental.
There's also a renewed interest in brass music in various movies, and bands playing ethno or world music. Bregović, for instance, does this for the last twenty years.
The trumpet festival in Guča is a big thing - no brass band worthy of its name fails to appear there. It's a big tourist attraction and a good place to get very drunk and stay so for a couple of days.