Yikes, this is a safety issue. Don't shorten the firing pin spring! This is most probably NOT the problem, and certainly not the solution. Possible reasons for the failure to fire include:
-Cutting too many coils off the mainspring in an effort to lower the trigger pull. (Replace the mainspring.)
-Too much metal removed from the hammer in an effort to speed up the lock time. (Replace the hammer.)
-A firing pin whose end had peened over and is catching in the firing pin stop. (Poor heat treatment of the firing pin.) (Remove the peened over area, heat until red, dip in oil to quench. Alternative: replace the firing pin.)
-Primers not fully seated in the primer pocket of reloads. (Seat primers until they bottom in the pocket. A Lee or other hand held tool is a good method. Otherwise, adjust your primer seater on your press.)
-On a Colt Series 80, having the trigger stop set too fine prevents full trigger travel to to push the lever to unlock the firing pin. (Don't know if STI has this product liability feature or not.) (Back out the trigger stop screw 1/8 of a turn and test for reliabile firing.)
-Rock hard grease in the firing pin tunnel. (Clean out the tunnel and use only light oil.)
-Extra hard lot of primers (not very often). (Change lots or change manufacturers.)
-A burr or metal chip in the firing pin tunnel from the hole drilled for the rear adjustable sight. (Clean out the tunnel and remove the burr/chip.)
The firing pin spring retracts the inertia firing pin. It is not strong enough to hamper the hammer blow.