Trying out a new hammer spring is a pretty easy test. Check out Numerich for your specific model to see if they have a mainspring.
Could be a few things, besides a weak hammer spring...
If the lock-up is getting loose (you'll usually be able to see wobble or a gap between the receiver and barrel), that can cause short pin impacts. This likely would be the end of the line for the shotgun. Just won't be worth it to replace and re-fit the lock up (unless you really like the shotgun).
The firing pin could be worn/broken.
The pin might be pitted and not moving freely.
Hammer spring could be weak.
Could have some junk/rust built up in front of the pin (or your pin return spring could be seized), or in front of the hammer face or body. Would cause short pin travel.
Chamber could be recessed a bit too deep, rim would seat too deep for even normal pin travel.
Hammer might be rusted (rust expands metal) and not moving freely on the pin, or within the receiver.
So, break it down, clean it all up, and try it. If it doesn't work, try the hammer spring replace.
