Mike Bullard is the only player to score 50 goals in a season, and record zero game winning goals. (In fact, every other player with 45+ goals in a season has at least one GWG, and only three other players have 40+ goals without a game winner). This was his 1984 season.
The most obvious reason is the 1984 Penguins were horrible (some have suggested they were tanking to draft Lemieux) and only won 16 games, and Bullard missed one of those wins. Rick Kehoe (who scored 18 goals) led the team with three GWG's.
Bullard generally played well when the Penguins won. He scored a goal in 9 of their 15 wins (three of those were two-goal games). Just none that were game winners.
Poor goal prevention appear to have cost him a few GWG's. On January 18th, he scored a natural hat trick. The third goal gave the Penguins a 3-2 lead, eight minutes into the third period. The Pens scored one more, then allowed three straight to lose in overtime. On January 3rd, he scored six minutes into the third to give his team a 5-4 lead. The Penguins then gave up three goals over the next six minutes.
I haven't done an exhaustive search, but at least twice he scored the tying goal in the third period, only to see his team cough up a goal. On November 20th, he scored the tying goal with just over five minutes left in the third, against a much stronger opponent (the Flyers). Bobby Clarke scored the OT winner. On February 5th, he scored the tying goal with 4:30 left (also against a far superior team - the Islanders), but Tonelli scored the winner less than a minute later.
(Actually it looks like he got two GTG - which is no longer showing on NHL.com. On November 3rd, he scored the tying goal with under 8 minutes to play in the third against Calgary. On February 25th, he scored the tying goal against the Blackhawks, this one with just 17 seconds remaining).
All this is statistical trivia. Most people accept that the GWG is a pretty meaningless statistic - but this is (somewhat) interesting.