This is the new designed behavior in After Effects CC 2015.3 (13.8) for audio playback when preview is not real-time.
In After Effects CC 2014 and earlier, audio was not guaranteed to be synced if preview was not real-time.
In After Effects CC 2015 (13.5), this was fixed so that audio would stay in sync. However, that meant solving the problem of how to play back the audio in non-real-time cases. The result was a delay between audio samples, to make up the time difference. This could result in stuttering audio, which many users told us was annoying.
In After Effects CC 2015.3 (13.8), a new audio playback architecture was added, the same audio playback used by Premiere Pro and Audition. This audio playback engine made a different solution possible: simply slowing down audio playback, rather than the delay/stuttering.
When audio playback slows down, the associated pitch drop occurs. This could, potentially, be changed in the future to include pitch correction. Please submit a feature request if you'd like to see this, or any other improvement to After Effects: adobe.com/go/wish
The problem is....mine still does both. It stutters, AND it drops in pitch. The pitch drop in tandem with the stutter sometimes causes some audio to just seems like it is being skipped over. I work with After Effects for my job every day, and had gotten used to the stutter, and have been able to work around it. This just adds another issue to deal with. The feature itself is not bad, but there should be a way to decide which of these 'unfortunate' situations I'd rather live with.
Can you provide more detail on the stuttering? There were some stuttering-type bugs (not related to non-real-time playback) that we fixed during the development of After Effects 13.8. If you're still experiencing similar issues, I'd like to get your results in front of the engineers.
A screen recording with audio would be very helpful here. Even video taken with your phone would suffice, as long as we can hear the result. Please send me a private message with a link to the file, YouTube, Dropbox, or however else you'd like to share it.