I too have this same problem. I bought my phone on 2/21/11. I noticed this exact same issue, and I too am in Chicago. I called Apple on 3/1, was told not aware of any data connection/loss issues, but they instructed to call VZW. I did and also VZW claims no issues. I still have the intermittant problem (once every couple of days) I haven't pinned to any specific activity, like I was surfing then a call came in and then after call couldn't connect, or was on WIFI, and then turned off, etc....I also haven't noticed if my phone still says 3G when I don't have data connection or if I have the circle instead. I am leaning towards the phone showing 3G.
I called Apple again today, says has heard of this issue, checked with senior advisor, and they also called VWZ that said yes has reported data issues in the Chicago area, but not sure if it is the phone and how it is working with data here, or if it is the VZW network. Said to toggle off airplane mode for a couple of minutes and then back on. That will do the same as powering phone off and back on, which is what I had been doing to get data to flow again. Told me if not resolved in a week or so, to call back and may replace phone.