Thanks everyone for recommending NWSL for a possible solution.  They told me today that they recommended using their steel rods and drilling the ends, which for a 3mm rod would be tricky.  Think I will work with brass tubing as suggested in the post by James from Florida.  Worth a try anyway
I also agree that finding a vintage "donor" would only postpone the inevitable and I really don't want to go that route.  I'll try the brass tubing and if that isn't satisfactory, I'll go with the steel rod and find a local home-based machine shop.
Thanks again, I appreciate all the responses.
Darrell

(James in Florida):  I think you have several options that may be do-able.  Worth puttering around anyway.  I'm going to Florida for a week and will try the brass tubing trick when I return. 
Thank You Sir, I sincerely appreciate your help.
Darrell

Sid:  Thanks for your prompt reply.  There are no hobby shops near where I live, but another post on the forum pointed me in the direction of NWSL for parts.  Perhaps I was misunderstood,  I didn't expect Bachman to keep parts for OOP Obsolete Models.  No more than I would expect Chevrolet to stock parts for vintage corvettes.  I was hopeful that perhaps a current model axle would be a mod or upgrade and fit my vintage trains.  I don't know if Bachman has kept track of how many trains they have made over the years, but there is a definite market for vintage Bachman parts out there.  And like many other "Vintage, Old Stock, and Classic" Collectables, they always have a "Holy Grail" or "Crown Jewel" that stood out over the years.  The Bachman 4-8-4's  I bet even Bachman has some of theirs displayed in a hallway or meeting room, somewhere.  Pretty much like this rare find on MSN earlier this week.  1969 Chevy Camaro SS: Rare Finds:   (http://www.msn.com/en-us/autos/enthusiasts/1969-chevy-camaro-ss-rare-finds/ar-AA9QGEX)  .  But a gazillion Camaro's are restored every year from parts from somewhere.  You see, Age is not necessarily queues to run the other way.  If it were, I'd be in a nursing home.  My Bachman trains (12 in all) came from a certified estate sale, and they had never been run.  A collector just bought them 40+ years ago, for display and if you've ever seen one of the Mint condition Vintage un-opened Bachman's and held it in your hands, Bachman's truly are a piece of model railroad history. Unfortunately, even sealed in the original box, the nylon axle deteriorates with time.  Hopefully someone will one day 3rd party parts for vintage Bachman's. Wish you the best in all that you do sir.  Thanks Again.

Does ANYONE have a "Fix" for the wheels falling off vintage 4-8-4 Bachman Steam Engines?  Literally Hundreds of Junk Bachman Vintage era Locomotives are flooding eBay each week, to unsuspecting buyers like me, and most all of these locomotives appear to be having wheel problems or broken nylon axels.  Does anyone (3rd Party) have replacement parts?  I have nearly $400.00 invested in "Mint Condition Old Stock" Bachman 4-8-4 Locomotives that do not run.  Bachman no longer stocks axels for the mass amount of locomotives being sold. Nearly All eBay sellers state "Returns not accepted".  I sincerely appreciate anyone offering a solution.  There apparently are hundreds or thousands of Bachman Vintage Locomotives out there that have wheel problems.