Google have updated the iOS version of their Google Play Music app fixing bugs in the apps. This release fixes disappearing downloads of songs and albums and fixes streaming issues. Maybe the disappearing issues is an iOS SDK issue as other apps have had this issue (BBC iPlayer).
The app is still iPhone only so on an iPad it doesn’t look particularly nice, hopefully that will be next on the fix list.
The app is free from the iTunes Store.
What’s New in Version 1.1.1.1147
– Lots of fixes around downloads disappearing and streaming issues