Entropy Loss of KDFs Am I losing any entropy when using KDFs, such as the ones in NIST Special Publication 800-108?

For example, can I derive 128-bit session keys from a (uniformly random) 128-bit master key?
When you use a PRF to derive a key, there is the potential for collisions. If you derived a 128-bit key from each possible 128-bit number, you'd expect some of them to collide. Specifically, you'd expect only about 63%  of all the inputs ($1-e^{-1}$) to appear as outputs.

That means you lose less than a bit of entropy even if the original key had the full 128 bits of entropy, like your random 128-bit string. With a lower entropy key you'd lose less. That doesn't matter in practice, since in the worst case it wouldn't even halve attack time. 127-bit security is enough.

In general, if you use a PRF to derive an $n$-bit key from one with $k$ bits of entropy, the resulting key will have at least $\min(n, k) - 1$ bits of entropy, approaching $\min(n, k)$ when $k \ll n$ or $k \gg n$.