The 2004 election was something of an aberration (sort of like Bush carrying Travis County in 2000); in every other election since 1992 it's gone for the Democratic candidate. Still, Cameron County is not quite as "blue" as other border counties, you can look up official returns for all Texas counties going back to 1992 at this website:
Election Results
Why it's not
quite as reliably Democratic is anybody's guess, my theory is that the county has more retirees from outside the region than the rest of the border, mainly near the coast and in the golfing communities. Harlingen also seems relatively conservative, or at least not as closely tied to the Democratic Party as other towns in the area. Together they probably dampen Brownsville's influence somewhat