The problem is that iPhone can't always receive incoming calls while it's transferring data over the EDGE network and EDGE can't be accessed while on a voice call–depending on which network you're on that is.
Apple Knowledge Base article #305711 states:
While iPhone is actively transferring data over EDGE—downloading a webpage, for example—you may not be able to receive calls. Incoming calls may go to voicemail.
iPhone Atlas reports that the issue has to do with what type of EDGE network you're connected to.
The “may not be able to receive calls” portion stems from the fact that there are two types of EDGE network types, NOM1 and NOM2. When your iPhone is connected to a NOM1 network, the data transmission will generally be interrupted, and the incoming call allowed to come through. When your iPhone is connected to a NOM2 network, however, the EDGE data transfer process cannot be interrupted, and the call will generally go to voicemail.
You can you tell which network you're connected to by dialing *3001#12345#* and tapping Call to bring up the Field Test Mode. From there select GPRS Information and find the entry for nom. A 1 in this field indicates a NOM1 network connection a 2 indicates a NOM2 network connection.
Since I learned about this over the weekend I've never been on anything but a NOM2 GPRS connection. Given my obsession with iPhone data, it now makes sense why I've been missing all these calls.
What about you, have you ever been connected to the mythical NOM1 GPRS network?