I would hazard a guess, that although the town Pittsburgh was originally named "Pittsbourgh" in the Scottish tradition [1], that the large amount of Germanic settlers in the region greatly influenced the pronunciation [2].

Kind of non-apropos to this answer though, NPR had an interesting story about how in the 1890s H's were removed from town's names and then re-added.

[1] http://en.wikipedia.org/wiki/Etymology_of_Pittsburgh
[2] http://www.loc.gov/rr/european/imde/germchro.html **source added