On a previous build I remember having the same problem the OP has, but it was long enough ago that I don't remember the solution.
+1 VLC, though I prefer Winamp's playlist management.
I don't use the playlist stuff. There are a few reasons I've stuck with Winamp. One is the graphic equalizer, not huge issue... sometimes it's useful for me, other times not so much depending on my equipment. The other is the fact that it's used by my MP3 editing software, Trackmaker. However, I could probably find another freebie MP3 slice-up utility I'm OK with, plus I can just opt to open MP3s with Winamp in the event I want to use Trackmaker.
I'm going to give Foobar and maybe VLC a spin and see how I do with them, maybe move on if I'm not satisfied and try some other audio players. Winamp is just not working for me in this usage. Even pausing playback before putting the machine to sleep does not prevent the problem.
Edit: Actually, looking I see that I already have VLC (installed Oct. 2011) on this machine. I'll see how it works, I've only used it for video in the past IIRC.
Edit2: VLC (at least the version from 10/12 I have installed, has the similar issues. Not pausing and pausing still don't let me resume from where I was in playback when taking the machine out of sleep. Foobar is somewhat better, but I have to pause first. However, I'm getting quirky problems such as messages like this:
Decoding failure at 16:11.110 (Network not reachable):
"\\thought2\wd20ears (e)\Mp3\TR20130429_010600.mp3"
I just got an unprovoked pause in playback for a few seconds that spontaneously resumed. Hmm. I wish I had a robust playback program. Maybe there's one out there.
Edit3: I tried my recording software, Total Recorder Standard Edition (not free but pretty cheap at ~$20). It has problems too. Maybe if I run actual server software on my server machine, maybe Windows Home Server, I have no idea. The machine's running WinXP Pro.
Edit4: Tried Windows Media Player, also impossible. Actually Winamp's behavior seems the easiest to live with among these, although it's terrible, it's the least terrible.
🙁 Maybe if I go to actual server software I'll get better results. Networking is not my long suit.