There may be differences in what the APIs do underneath the hood. The OS only allows end-user applications to basically make "requests" to keep the system awake, but can decide to ignore the request. Assuming that this broke and nothing changed in MC, then it would seem that El Cap handles things differently.
Can you test and try to determine if the issue is specific to the NAS or to DLNA? The easiest way would be to copy a set of files to the internal disk, and play a long playlist from there only, and see if it happens. If it still happens, that would seem to rule out the NAS (and then disk sleeping as the issue) and point to the network interface going to sleep instead.
My guess is the Network interface. As I said above, I can't wake my system with USB input anymore through my KVM on El Cap (and it worked with Yosemite and many of the El Cap betas), so I know there have been changes to the underlying Sleep APIs (or bugs where things are broken, which might be more likely).