Around here, in lovely Chicago, the roads are awful. Plain and simple.

Recently, I had the drive-side chain stay on an 80's Raleigh (steel stay) fail on me. I don't think it had ever been ridden much before I got it, so I am the one who killed it. Of course, this has me very concerned about my new steed. Tonight, I went for a lovely little ride, seeking out the better roads in the area. Still, I hit a few rough spots, and always do on my rides. Hitting uneven pavement at 20+ mph is no fun. Riding on rough roads and hitting the occasional pothole simply can't be avoided (unless I don't ride, which isn't really the idea). I'm worried the same thing that killed the Raleigh is going to happen to my new bike (although I admit that the day it died I did ride a rough trail with it; wasn't familiar with it, and it seemed fine at first)

How do you guys deal with bad roads? I am riding my tires with PSI on the lower end of recommended pressures. Should I be as worried about my nice new Bianchi as I am, or as long as I keep it on pavement, even if it's rough, will I be ok? I admit to abusing the Raleigh a bit, but if this one fails anytime soon I simply won't be able to replace it.

A 20+-year-old steel bike (I have two of them) is apt to have suffered some rust damage along the way. If you still have the frame, look inside to see if the stay rusted almost through before it broke. I have a mid-'80s Trek I converted to singlespeed a few years ago, and I really like it, but I'm increasingly reluctant to ride it because, while the outside looks good, I don't know what's inside the tubes.
On the new bike, miss what potholes you can, "float" over bad spots by standing and absorbing shock with your legs and arms, and run the biggest tires you can at fairly low pressure. The bike I ride most often in the city has 700x37 tires, and most of the time I keep them at 70psi.

Check with your LBS but some manufacturers have a much longer warranty on the frame than the rest of the bike. If so then if it dies the warranty should cover it.

On the Paris Roubaix, the Cervelo team used the RS with different forks and bigger tires than the standard 700 x 23. That route is bone jarring, like your Sheridan Road trips.