iTunes not playing songs from iCloud in Match
I keep 50% of my music library on an external HD. I subscribed to iTunes Match to be able to access my entire library when my HD isn't available (traveling, HD in sleep mode, etc.). But iTunes won't play any songs that are stored on my external HD when the HD isn't available, even when the songs were purchased on iTunes, and even when iTunes has matched them and shows them as "purchased." When I try to play the song, iTunes says the external HD isn't available, and offers to allow me to locate the song (which is impossible because I'm not near the external HD). Why won't it use the copy that's stored in iCloud? Isn't this the whole point of iCloud, i.e., to allow me to stream my music library from anywhere?
I have an active internet connection, and I've already updated Match and turned it off an on again. But iTunes won't play any of my songs from iCloud; only from my Macbook hard drive, which certainly isn't the point of Match.