** IT'S THE NETWORK **
I have bad news for those who think that swapping the phone for new HW will fix your problem, it won't. (I have swapped mine and swapped my SIMs) as you've read my rants over the past 2 months. I have bad news for people who think that switching to an Android phone will fix your problem, it won't. One side benefit however is that the Android phones are capable of 3G/LTE simultaneously, so you can do voice and data at the same time, which is not possible on the VZW iPhone 5.
The problem is primarily the network. in my case, the Verizon Wireless network. In others case, whatever network you are on. Sure, the iPhone 5 has some issues, specifically it has exhibited more trouble than other phones in the most marginal coverage areas, but the real problem is the enormous number of marginal coverage areas throughout the VZW LTE network.
I can state this confidently because I spent today with 2 of the 3 top VZW Android phones, my iPhone 5 (VZW) and my AT&T GS 3.
While some VZW phones behave a little better than others, none of them locked solid LTE throughout the day in Metro Boston. Even when there were times when all 3 had good LTE signal strength, all still underperformed AT&T by a wide margin. In every marginal coverage area, every VZW phone had marginal coverage, none of these marginal coverage areas were AT&T marginal coverage areas. HTC DNA seemed a little better at locking 4G LTE, but also visited 3G (EHRPD) plenty. The RAZR MAXX HD had the strongest signal of all 3, but spent even more time on 3G than either the iPhone 5 or HTC DNA and all phones visited the 1X network (o on iPhone 5) on more than one occasion. In the most marginal coverage area of all (my house), the iPhone 5 came back to LTE sooner than either of the two Android phones, the RAZR MAXX HD took a while to come back to LTE, but did, and the DNA which has been the best on marginal 4G, is still stuck on 3G (10-15m and counting). The iPhone 5 definitely spent a little more time on 1X (o) than either of the Android phones. The Android phones did seem to hug 3G in the most marginal coverage areas while the iPhone 5 seemed to stick on 1X. Do keep in mind that once the phone hits 1X, the switching back to LTE/3G is ugly (not a nice handoff), vs. with EHRPD, the 3G to LTE transition is a little smoother.
I also ran the "Pandora" test that InkStrategy was talking about and had no problems w/ the iPhone 5 streaming Pandora between towns and even when my phone transitioned from LTE to WiFi. Unrelated to the music streaming, there was one instance where my iPhone 5 refused to pass any data in a strong LTE area and I did have to toggle Airplane mode to get it to play nicely again. This instance seemed like an iPhone 5 SW bug.
Save yourself the frustation, if you are not happy with your signal strength, find another carrier. In my case because of the # of family phones I have, I intend to keep VZW for these lines, but I am not happy with how they perform vs. AT&T (EVERYWHERE).