Monk's alternative can be done, but I think you should try to keep your rifle in as close to original shape as possible.

Remove the trigger guard assembly from the rifle.  detach the floorplate, if it has not already done so by itself.

You will note the floorplate latch (to the rear of the TG assy)  It was made to be actuated by the tip of a bullet.  Using a similarly-shaped object which will not mar the steel/finish of the rifle, try moving the floorplate latch  back and forth in its recess.  Most lilely it is either gummed up with grease/cosmoline/junk, or the spring for the latch is N.G..  Flood this area with de-greaser, preferably under pressure.  Let sit overnight.  Do the same thing next day.  Use compressed air to blow out the hardened grease and junk that is probably gumming up the spring-loaded latch mechanism.

If this does not work (probably won't without compressed air), then drive out the small pin which holds the latch mechanism together, and clean the latch mechanism recess thoroughly along with all the parts.  Cover all parts with a light film of oil, and re-assemble.

You will need to have the right parts, and a properly sized drift punch and small hammer.  Easy job.  After you have done it once, it is a ten-minute job at most.

I suggest you order a new pin and spring from Numrich before you start. as they are easily damaged/lost.  Their  website exploded diagram will also help in assy/dis-assy.  Might want to inspect the  old latch itself, in case it has been bunged up.

Now is also the time to order any other parts you might want.  Springfields were known to have  easily damaged front sight blades (no sight blade guards) and they broke firing pins, firing pin collars, and strikers.  Get the little pin for the FS blade, too.

Quoted: I took the floor plate out and the latch doesn't look damaged but it doesn't seem to grab well either. I don't see any grease or dirt build up. I'll disassemble it later to check inside the latch mechanism. I noticed that there is a little pin hole on the floor plate and part of the trigger guard. Am I missing a piece to my rifle?? I'll check with Numrich Gun parts to order some spare parts.

I suggest you won't know the whole story until you completely dis-assemble the latch.  My guess is a worn, 60-year-old spring, maybe a damaged latch or floorplate, and an accumulation of gunk within the latch recess.  I'll bet that a cleaning and new spring will set you right, unless one of the other parts shows signs of excess wear-- not likely, but remotely possible.

Don't know about the pinhole business, can you elaborate?

Ahhhh... The plot thickens....