Own a 02 Jeep Liberty. had top-of-the line Michilin tires mounted on
11/24/04 and on 3/6 the right front wheel fell off on the 495 Beltway.
 My daughter managed to get the vehicle to the right shoulder without
injury or damage to any other vehicles.  The car was towed to Henry
Gay Jeep, visual damage estimated at $1100.00 and all of the wheels
were loose. Mr. Tire is saying that tires not torqued correctly will
fall off in three days. Can someone tell me why this happened?

Tires are not "torqued". Lug nuts are torqued (tightened). Lug nuts
hold the wheels on your car that the tires are mounted on. I don't
know where the "three day" fall off rule comes from. If lug nuts are
loose (not torqued), they could allow a wheel to come off in a matter
of hours or months depending on exactly how loose they are. I think
Mr. Tire is blowing smoke up your exhaust pipe.

I've been in a passenger in a car twice when that has happened

- once it was just a disintegrating car

The other time I strongly suspect sabotage

I suspect that the length of time it will take for the wheel to come
off would depend upon just how loose the lug nuts are, how many miles
are driven, what the speed of the vehicle is, and the road condition.
It seems likely that driving fast on a bumpy rural roadway would
rattle the lug nuts off a lot faster than doing 25mph on a smooth
urban road. The "three day" dictum sounds like BS to me.

I once had a wheel come off my 1968 Volkswagen Beetle just hours after
getting it back from the shop. Turned out that a new guy athey'd
screwed the lug nuts on by hand, and forgotten to tighten them
mechanically.

In my comment above, "athey'd" should read "had."

Certainly the torque issue applies to the lug-nuts, but you also need
to consider the tire balancing as well. Should they be improperly
balanced, the whell begins to shift fron/tback, left/right, possibly
stripping or even disengaging the nuts.

It's actually a common issue with Jeeps, from what I understand. I had
a 1990 YJ Wrangler, and the same thing nearly happened to me (same
wheel). The problem is that if the nuts aren't torqued correctly, the
wheels on the right side (usually the front right) will loosen up.
This has to do with the wheel spinning in a clockwise rotation and the
nuts wanting to spin in a counter clockwise motion (loosen up).

With my Jeep it was always a common practice to tighten the wheels on
initial installation, then check them again about a week later to make
sure they were still tight.

Another problem could be after-market/aluminum wheels. The softer
metal causes "settling" when initially torqued, and normally requires
a rechack after about 100 miles of driving. There are some pretty good
write ups here that hopefully will help you out.

http://www.jeepforum.com/forum/search.php?searchid=456405