Burning off last years growth is the the reccomended maintenance for buffalo grass.

The brown you see is not dead grass...just dormant grass.
Buffalo grass goes dormant like traditional lawn grasses with the onset of cool fall weather. It will also go into a summer dormancy in periods of summer drought to protect itself.

Vera

The brown growth from last year will probably inhibit new growth by shading it and by keeping the soil surface cool.

If you can't burn, a spring mowing to remove the past year's growth would probably be beneficial. I don't have personal experience with buffalo grass, but this is a generalization from other warm-season grasses like little bluestem and prairie dropseed.

Mowing will not harm the living parts of the plant, as long as you don't mow so low as to scalp the soil surface.

...some info

Here is a link that might be useful: Buffalo Grass

I remember a post awhile back where there a guy had buffalo grass and tested burning or not burning...

Here is a link that might be useful: buffalo grass old thread

I posted a question back in '04 about our buffalo grass, weed problems and what to do. I'm happy to report that our buffalo grass is doing fantastic. The first two years were frustrating with weed problems, especially crab grass. We are able to burn, and that's what we've done since the first year (2003). We still have a few weeds, but pulling them seems to be the best remedy during the growing season. They come back much weaker due to the smothering effect of the thick buffalo grass.

We are also in our fourth year for our native meadow, having sown nearly 75 species of native forbs and grasses over a 2 1/2 acre patch 100 feet from our house. The first year was nothing but weeds, but I kept it mowed to a height of 8-12" throughout the spring and summer. There was mostly pig weed and foxtail, some of it going to seed. I couldn't see any indication of anything native coming up, and it was disheartening. We tried a burn the following spring of 2004, but there wasn't enough vegitation to support a good burn, the results were spotty. During 2004 we were beginning to see a few native plants from what we sowed - upright coneflower, black eyed susan, purple coneflower, mexican hat, and canadian wild rye with others making appearances. Weeds were still a major problem, and I purchased a circular steel blade for my lawn trimmer to cut the weeds at the base. This was a great help, but the weeds were still a major problem. In the spring of 2005 we were able to get a good burn over 95% of the meadow, and this really helped in the weed fight. Weeds were still present, but we could see more and more natives showing up, and fewer weeds. This spring we were able to get another nice burn, and the meadow looks great! The areas that burned good are completely weed free. There are even bare areas which would normally be covered with weeds that are completely weed free. We couldn't be happier with our project. There are still some weeds present, but they are losing ground and keeping them in check is much easier. I am a true believer in burning wherever possible. I'll post some pictures later if I can figure out how to do it! Jim