On May 19, 1998 at 2030 central daylight time, a Cessna 182, N507SD, was substantially damaged when the engine lost power during approach to landing. The airplane landed in a field and nosed over during landing rollout. The commercial pilot was not injured. The 14 CFR Part 91 flight departed Independence Municipal Airport, Independence, Missouri, on a local skydiving flight. Visual meteorological conditions prevailed and no flight plan was filed. The pilot reported that she had departed at 2000 CDT with a student skydiver and a jumpmaster. The skydivers exited the airplane at 12,000 msl. The pilot reported that as the airplane was descending through 4,000 feet msl it started loosing power. She leveled off, pulled carburetor heat on, and switched fuel tanks. She reported that, "Upon restart the engine backfired and quit." She reported that she trimmed the airplane for best glide (80 mph) and flew directly for the airport 2.5 miles away. The pilot reported that at .5 miles from the airport she realized she would not make the runway so she decided to land short. She set 10 degrees of flaps and landed in a field. The airplane hit a wooden fence post during landing roll in the muddy field it nosed over. During the inspection of the airplane, no airframe pre-mishap discrepancies were noted. The engine was inspected. Engine continuity was established to the accessory section and a thumb compression check was accomplished. The spark plugs were removed and appeared gray in color. All magneto leads produced spark upon manual rotation of the propeller. An examination of the induction system found that on the left side of the engine, the balance tube had separated from the intake manifold tube assembly. An orange rubber sleeve and two metal hose clamps on the intake manifold tube assembly were noted. The carburetor heat was found in the off position. The propeller exhibited aft bending on both blades. There was no visible damage noted to the spinner. The engine was test run. During the first test run, the induction system balance tube coupling was left disconnected as it was found and an attempt to start the engine was made. The engine started but would only run when the throttle was continuously pumped so that the accelerator pump could pump fuel in the induction system. With the open induction system, the fuel/air ratio was lean. The engine was shut down and the balance tube coupling was connected and the engine restarted. The engine operated and did not require continuous pumping of the throttle. The engine was run up to 1,700 RPM and a magneto check performed. The magneto drops were 75 to 100 RPM with no difference between the magnetos. The engine ran smoothly at 1,700 RPM with no missing or backfiring. The examination of the induction system balance tube coupling indicated that the balance tube did not line up with the intake manifold. No other pre-impact mechanical anomalies were noted on the engine.