There is a design feature that can cause an Ithaca to malfunction if the gun is not maintained. The left hand shell stop has a spring behind it and rides on a pivot. It the spring becomes weak, the pivot or channel the shell stop rides in becomes dirty/gummed up, then the gun can definitely have issues with double feeding, spitting shells on the ground, etc.
There is also one other problem with the same that came about due to an engineering change. After the gun design was acquired from Remington (yep the original Ithaca 37 design was first put out by Remington in 20ga only), the magazine tubes were made with a pressed in bushing at the end. The inside diameter of this bushing was such that it controlled the presentation of the shell rim to the rt and lt shell stops in a very precise manner.
Due to someone's infinite wisdom, probably some bean-counter, this design feature was changed to a simple roll crimp. This enlarged the magazine tube (now I am going to refer specifically to 16ga guns as these are what I deal with and restore) by .030 overall or .015 on a side.
You don't thing this means much, but if you take a shell rim with minimum tolerances on its OD and run it through a tube that is now sloppy, the tangent point of the shell rim can miss being grabbed by the left hand shell stop and pop out on the ground.
I have machined up .015 thick wall thickness bushings to go inside a current made magazine tube (roll crimp design one) to adapt it to a 1970 vintage receiver (before the design change was made). With the insert, the gun feeds shells precisely into the shell stops.
As far as dirty conditions or weak springs, I received one that had both. It would spit shells on the ground, misfeed etc.
There is a very simple 2 part fix for this. Take the buttstock off and get yourself some gunsmith in a can, ie: spray brake cleaner. Your take the buttstock off so you don't fill up the inletting area with any more gun that it already has.
Then spray the insides out and clean the gun, then re-oil.
If this doesn't fix the condition of a gun that used to work correctly, then replacement of the spring is in order. The spring is only a couple dollars from Ithaca Gun. Shipping is probably more than the cost of the spring. I was able to procure a few locally.
In the early guns, you will need a jeweler's / micro screw driver to get the screw pin out. Do not bugger that up. And when you re-install it, do not force it in and bottom it out. Gently screw it in until it touches and then back it off a half turn (even 3/4 turn).
Later guns use a pin assembly to hold the shell stop in. You have to take the slide/bolt assembly out to take this apart.
The spring simply pushes into a machined recess in the shell stop. I don't remember at this time whether or not one end of the spring was different sized, sometimes I just work on things and adjust as I go along as I am assembling parts. But keep in mind you might need to swap it end for end. It will go into the recess and stay there for you to reassemble.
One of the best things that owners of older Ithaca guns can do for themselves is learn how to take the gun apart (use good gunsmith screwdrivers, not a set from the Bubba store) and give it a good cleaning and relube it. I put gunslick grease on the contact points, but your mileage may vary. I have also come to really like Clenz-Oil. Works really well for removing gunk, dried oil, etc.
You won't have to take the trigger pack apart, but simply give it a good spray cleaning. You could even soak the parts in kerosene.
Another place that is overlooked is the inside of the magazine tube. I have cleaned the older ones I have and was surprised at the amount of rust / crud that gets in there when people don't clean them out.
Take out the magazine tube spring and shell follower. Get yourself a 3/8 or if you have a drill that will handle it, 1/2 in wood dowel. Cut a slit in the end and push some 0000 quad-0 steel wool into the slit. Soak the steel wool with oil and run it up and down in the magazine tube. You may have to change the steel wool, spray it out with brake cleaner, etc depending on where the gun has spent it's life and rusted/got dirty.
Once it is clean, oil the inside of the tube with a good rust-preventative gun oil, and do the same to the spring, clean and oil it and reassemble the gun.
dave