Here is my problem.  All suggestions will be gratefully pursued.

On Wednesday, while out shopping, I came out to start my bike and found it dead.  Serowbot was kind enough to come and give me a jump.  The bike started right up.  I ride it about 20 miles before returning home.  In my driveway I turned the bike off, turned it back on and hit the starter button.  Dead bike.

On Thursday, I pulled the battery and took it to a local shop to get a replacement.  They charged and checked the battery, and told me that I did not need a new battery, that my battery had tested good.  I came home and put the recharged battery in my bike and hit the starter.  It fired right up.

Today, Serowbot, George, Jim, and I rode up Mt. Lemon.  I was about a 70 mile round trip, with a couple of stops in both directions.  The bike ran and started without a hitch.  On the way home from the ride, I made a quick stop at a store.  When I came out, the bike was dead.  This time it was George who came and gave me a jump.  Bike started right up and I rode it home.  

RIght now the bike is in my driveway, and the battery is on a charger.  Obviously, the battery is not recharging.  I do not have a clue about what to do or check next.  Please make suggestions.

Thank you

Ha, rectumfryer. Possibly the rectifier is dead as well - hopefully it's not the stator. If the connections check out OK, verify the stator is working before you replace the rectifier. If you have a volt-meter, set it to an AC setting that's over 15V, start the bike, and then check across two of the yellow wires plugged into the rectifier. Should be reading well over battery voltage (voltage depends on stator winding style and RPM of bike but it should be well higher than battery voltage). If that is fine - no problem with the stator - rectifier is shot. Pretty much any 3-phase self-exciting rectifier will work if you're looking for a cheap fix and can do some wiring. The self-exciting rectifiers have 3 wires in from the stator and 2 wires out - positive and negative.

take off your seat and pile on, and you'll see a finned square thing with 2 bunches of wires going to it.  remove the connectors and plug them back in.  Put your seats back on.

Rectifier,...  I know where there is a spare one,...
Why don't we swap it out?...

Me thinks, yer bike no likey shopping. Take it to a ball game or bull fight and see how that goes...

Not a happy outcome, I only had 45 K on that bike, but I want to give a very sincere "Thank You" to everyone who made suggestions.  You put us on the right track, even if we didn't like where it ended up.  Guess that I will be without a bike for a while.  Grrrrr.

good thing there's a mechanic in the house.

Hate to see that make a parts bike out of it, what about a junk yard part?
Is the labor too much? Doesnt that take a special tool?