Brian,

There are a lot of elements that go into decision making in airplanes; takeoffs are among some of the most important decisions we make, and landings aren't far behind. The decision regarding whether to return or press on depends on weight, length of runway, condition of runway, weather, maintenance and parts availability, and a host of other factors that might make flying to another location more or less desirable than returning to one's departure airport.

Rejecting a takeoff is one of the most potentially hazardous things we can do in a large transport-category airplane. A blown tire on takeoff, especially in the high-speed regime, makes continuing the take off much more desirable in most cases, than risking stopping; a lot of runway is already behind the airplane, it's moving fast, braking capability is reduced with the tire out, it's the heaviest it will be for the duration of the flight, it will require heavier braking and a larger demand on the brakes to stop, than to come back with a long runway in front, at a lighter weight, etc. There may be times, however, when stopping is preferable, and that may be a judgement call that the pilot in command must make in real time when the tire goes. There isn't a "tire just blew" light or annunciator on the flight deck, so a bang, vibration, or other indication may not be interpreted correctly, or even necessarily at the time, and after eighty knots (in most cases), the rejected takeoff will be in the "high-speed" regime. That's usually reserved only for an engine failure, a fire, the aircraft is unsafe or unable to fly, or something like a predictive windshear annunciation (something the radar warns about in bad weather). A blown tire may not give an indication that tells the crew the airplane is unsafe or unable to fly. Without a master warning light or annunciation, or other indication, or engine indication, or fire indication, the crew may see an aircraft that's accelerating normally, approaching decision speed, with good engines and good directional control, and have no indication that rejecting the takeoff would be required.

If the airraft takes off and a tire falls off (United's loss isn't the first), that's a serious mechanical concern. That isn't simply a failed tire. What's occurred to cause the tire to separate? There's a lot more holding that wheel assembly and brake assembly on the airplane than just a big nut. What other damage has occurred? This is also a concern with a failed tire, which may have damaged the airplane structure, but when we have a component separate from the airplane, and we know it, perhaps we don't want to attempt to raise the landing gear. Do we have brake lines hanging out that might cause the gear to stick in the retracted position? Are we experiencing a hydraulic loss? What maintenance wasn't done that caused the wheel to separate? What other maintenance might not have been done, that hasn't manifest itself yet? Bird in the hand. We're by a long runway, long enough for us to takeoff at our heaviest weight for this trip, so it's long enough to land, especially if we dump fuel and return at a lighter weight. If it's a place like LAX, it's got good crash rescue and support facilities, good approaches, etc. The crew is fresh, at the most rested and alert they'll be for the entire trip. If there's a good time to handle an abnormal situation, this is it.

The good news is that tires don't blow out, or fall off, very often. Both are quite rare, though they do happen. I had a wheel come off an airplane in Iraq some years ago, and I was quite happy to have a long runway to myself, for a successful, quiet landing. It doesn't happen often, but it does, and when it does, we must look at all the elements and how they apply to us, to decide how we'll handle it. In most cases if we know about it, (a blown tire we may not kow about, vs. being alerted to a wheel assembly that just separated from the airplane, for example), we're not going to press on. A conservative, safe approach is to land at the nearest practical airport, depending on the circumstances, but in all cases, we'll be looking to the safest course of action, given what we know at the time (or what we think we know at the time).