Approach minimums exist for a reason
Instrument pilots know that every approach has a hard altitude, a point at which a decision must be made to either continue the descent or execute a missed approach procedure.
On March 7, 2003, the pilot of a Beechcraft Bonanza died when he chose to descend below the approach minimums and hit trees near the approach end of Runway 10 at Baldwin County Airport in Milledgeville, Georgia.
The flight was handed off to Atlanta Approach from Atlanta Center at 9:59 p.m. One minute later, the pilot was cleared to the AZNAX initial approach fix, told to maintain 2,400 feet until established on the approach, and then cleared for the GPS Runway 10 approach. At 10:12 p.m. the pilot called Atlanta Approach and reported that he had executed a missed approach and requested a second GPS approach to the same runway. About half an hour later, the pilot called Atlanta Approach to report another missed approach, and asked for a third clearance for the GPS Runway 10. At 11 p.m. a local resident found the airplane burning in an open field less than one-half mile from the airport.
On the first approach attempt, radar contact was lost 4.06 miles from the airport at 1,700 feet. On the second, contact was lost 5.06 miles out at 1,400 feet. During the third approach, radar contact was lost 6.6 miles from the airport at 1,200 feet. Altitude minimums for the approach requires staying at or above 2,000 feet msl until reaching the final approach fix (MIZYU), which is located 5 nautical miles from the end of the runway, and not descending below 900 feet msl (516 feet agl) unless the runway is in sight.
Weather at the time of the accident consisted of overcast clouds at 300 feet (684 feet msl), visibility 7 miles, and winds 70 degrees at 6 knots.
The NTSB determined the probable cause of this accident was the pilot's improper IFR procedure by which he failed to maintain the minimum descent altitude and his failure to maintain obstacle clearance.
Given the progression of the altitudes recorded by radar during each approach attempt, it's possible that the pilot caught a glimpse of the airport on his first approach, and was sneaking lower in an effort to find the airport. On the third approach, the Bonanza was 800 feet below the minimum altitude for the final approach fix, which was still 5 miles from the airport. A better choice would have been to divert to an alternate with better weather or a precision approach.
To learn more about the regulations for IFR flight, take AOPA Air Safety Foundation's IFR Adventures Online Course.