Problems down shifting on front mechs is often caused by dirt and grit making the mech pivots too stiff for the return spring to return. Spray the mech at all the hinge points with spray lubricant, WD40 or whatever you have and then grab hold of the mech and manually move it through its full range in and out. (Shifter in low gear position) Initially you may find it is quite stiff - but keep at it, and add more spray a few times too. The important part is taking the mech over into the low position as far as it goes.
I think this is more likely to solve your problem than the previous suggestion of cable renewal. Rear derailleurs are much more prone to cable drag than front derailleurs due to the greater cable length. If you want to check the cable though, put bike onto high chain ring and then move shifter lever over to low while pedalling. Now check the cable at the front mech. If the cable is slack - but the chain hasn't moved over to the inner chain ring either the mech is stiff as I believe or the Low limit screw needs adjusting by turning it anti clockwise. If on the other hand, when you check the cable at the mech it isn't slack, it could be that the cable needs slacking off or more likely, the cable is binding.