Via Baseball-Reference.com's Play Index Pitching Game Finder, since 1954, RP with the most career "L" games where they faced just one batter in the game:

                   Games Link to Individual Games
+-----------------+-----+-------------------------+
 Mike Myers            7 Ind. Games
 Steve Kline           6 Ind. Games
 Dave Rucker           5 Ind. Games
 Ray King              4 Ind. Games
 Norm Charlton         4 Ind. Games
 Gary Wayne            3 Ind. Games
 Greg Swindell         3 Ind. Games
 Scott Schoeneweis     3 Ind. Games
 Ricardo Rincon        3 Ind. Games
 Dennis Powell         3 Ind. Games
 Dan Plesac            3 Ind. Games
 Bob McClure           3 Ind. Games
 Sparky Lyle           3 Ind. Games
 Graeme Lloyd          3 Ind. Games
 Dennis Kinney         3 Ind. Games
 Mike Jackson          3 Ind. Games
 Mike Holtz            3 Ind. Games
 Mark Guthrie          3 Ind. Games
 Rich Gossage          3 Ind. Games
 Tony Fossas           3 Ind. Games
 Eddie Fisher          3 Ind. Games
 John Candelaria       3 Ind. Games
 Jim Brewer            3 Ind. Games
 Tom Bolton            3 Ind. Games

Mike Myers has 24 career losses - and in 7 of them he faced only one batter.  Then again, Myers pitched in 314 games in the big leagues where he faced only one batter in the contest.

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