One problem related to engine burning oil has been reported for the 1998 Chevrolet Blazer. The most recently reported issues are listed below.
Vehicle burned over 9 qts of oil in 3-4 months. First noticed 12/98, dealer began checking and testing. Finally, in April - may 1999, it was determined that vehicle was burning about 1 qt every 300-400 miles. They finally agreed to replace entire engine because they could not locate source of problem. The night before carrying it for service, vehicle lost transmission power. The dealer had to tow the vehicle in the next day. At this time, they not only replaced the engine, but also the entire drive train/transmission system. They still have no idea what caused the failures on such a new vehicle. I tried to get a replacement vehicle since the first failure was around 5,000 miles, but the gm representative refused and only offered to replace the engine and transmission. I don't think I'll ever fully trust my vehicle now, but can't afford to trade at the moment.