Front Friction Shifter Problem
With friction shifters this is usually caused by one of two problems:


Loose Shifter Screw: Friction shift levers usually have a wing-nut-screew used to adjust the tension and friction of the lever against the mounting housing.  Tighten this screw, but not too tight or else you can't move the shift lever.  You can also take the shifter apart (noting carefully the order of the parts) and clean everything with degreaser.  DO NOT LUBE - you are trying to regain friction, not remove it.



  Edit re. ʍǝɥʇɐɯ  - After you adjust everything you may find that the shifter screw continues to come loose almost immediately - in that case you may want to use a little 'adjustable/removable' Loctite on the screw, assemble, and let it sit for a while before using.  That should help hold everything together.



Cable Friction: Often there will be one or more points of friction on the cable route.  This could be in the housing, or in the routing channels under the bottom bracket.  As you apply pressure to the pedals the frame flexes, pulling the cable one way, but then the friction stops it from sliding back.  Check and clean your housings and routing points, especially at the bottom bracket.