While trying the Bitcoin Wallet for Android I have tried to send 0.001 BTC to the phone (in this case with 0.0005 fee) and back (this time without fee, because the app does not implement fees in the moment).

The transaction with fees went through nicely, but the backward payment without fees did not arrive even after a day. I searched the unconfirmed transactions on
http://bitcoincharts.com/bitcoin/
but cannot find it. It also does not show up in my PC-client. Is it possible that such small transactions without fee are dropped completely by the network? Are there any documents I should read?