Am I overloading the power supply?
Those chips draw so little power the odds are > 99% that you're not.
The most likely culprit is noise: depending on how the sensors are wired, you could be creating a giant noise antenna, with each sensor you add increasing the noise a little until it eventually overwhelms the signal.
Did you add the external pull-up, as recommended on the Playground page
Are the cables to the sensors shielded (or, at least, twisted pair like Cat5)?
There's an app note on the Maxim site
with info on how the pros do 1-Wire networks. You may find that helpful.