I have an iP9 as well, and I have had that problem intermittently. The song starts to play, but after a few seconds, the buzzer sounds.
I have done some experimenting, and this seems to only happen with quieter songs, or at least songs that are quiet in the beginning, since this doesn't happen when it plays loud songs. I put only Bolero, by Ravel, in my "iHome" playlist, which starts out very soft, but ends very loud. It would start to play, but then the buzzer sounded every time. Then I put the fourth movement of Mahler's 1st symphony as the only song in my "iHome" playlist, which is very loud in the beginning, and the buzzer did not sound.
I'm thinking that the buzzer is a "safety" mechanism that it uses if it thinks the song is too quiet to wake you up.
My solution now would just be to only put loud songs in your "iHome" playlist. I don't know what the difference is between loud and soft with respect to the iHome, so you'll have to experiment with what songs will be soft enough to cause the buzzer to sound.
My hardware: iHome iP9 and iPod Touch 2g with OS 3.1.2.