I've had exactly the same problem with my Pre3 this week and it had never done this before. The only thing I could think had changed was earlier this week I took out my SIM card to use to activate my daughter's Pixi Plus. Since putting it back in my Pre 3 I got this dropping the network connection problem so I guessed it must be an issue with the SIM card contacts. Wedging a slip of folded paper between the back of the SIM card and the SIM card holder in my Pre 3 seems to have done the trick for now... Let me know if it works for you.
I had a similar problem with my Pre 2. It turned out that the "Network Type" in Phone Preferences needs some fiddling. Sometimes, setting it to "2G Only" works, at other times "3G Only" helps. Setting it to "Automatic" at times causes problems in my area. Maybe it is that some areas have better connectivity with 2G.
I realised what caused the problem (at least in my case) when I started facing problems after I upgraded to 3G
Seems the problem for my Pre3 was a damaged SIM card. I got Orange to replace my SIM card I got no more dropping of the network. I can only think that repeated removal of the SIM card scratched the gold contacts and damaged it somehow. I'd inserted the card into a Pre2 and a Pixi Plus which both have a "vertical" rather than "horizontal" SIM card holder. Perhaps the scratches on the card in two directions caused the problem? Anyway my Pre3 is working fine again now.
I have this problem, too, on my Verizon Pre 3. I've been trying to figure out what's been causing it, but haven't been able to do so yet. Toggling airplane mode generally gets the connection back, but not always.
It seems that changing the 'Network Type' has helped me. I always used '2G only' at home since the 3G network is weak here and to save battery.
Now I changed it to 'Automatic' at have no more connection losses.
In the meantime I've switched back to '2G only' and the connection is still stable.
When I changed the 'Network Type' to 'Automatic' I also put a piece of paper at the back of the SIM card, so maybe that did the trick?!