Songs keep repeating when I shuffle a playlist

On every iPod and iPhone I've ever owned:

I open a playlist and set it to shuffle. It does. I pause a song, put the device away, and press play a few hours or days later. The device remembers what I've already played so I don't hear the same song twice until I get through all, say, 250 songs on the playlist (unless I select a different playlist, manually select a song on the playlist, or close the iTunes app on my phone). As an illustration, using my iPhone 6 (still on iOS 8.3) last month I spent a week of commuting time, about 45 minutes a day, listening through a playlist and never heard the same song twice.

On my iPhone 6 since updating to iOS 8.4 (12H143):

I open a playlist and set it to shuffle. It does. I pause a song, put the device away, and press play a few hours or days later. It doesn't seem to remember what it's already played, so I end up hearing the same set of about 25-30 songs (with occasional randoms thrown in) every time I pause, put it away, and press play a few hours or days later.

Why doesn't Music seem to remember what it's already played? Is there any way of fixing this, or working around the issue so I don't have to keep hearing the same songs on a playlist?

On a possibly related note, I just connected my phone to my computer, and noticed that several of the songs that keep getting repeated show up in iTunes as having never been played. Has Music/iTunes stopped counting, or is this feature just not working any longer?