Hm. Sounds like you have a battery drain going on. Are you sure you are turning the key off in the correct position? (OFF, not PARK).

sounds like it's not producing electricity

do you have a volt meter?  get one.

you should have at least 13 something volts, rev it up should get near 14 at the battery.

disconnect the line from the stator to the rectifier.
at 4000 rpm should be 100 vac across a couple of leads.

http://suzukisavage.com/cgi-bin/YaBB.pl?num=1367026776/0#0

When I bought this bike from this old guy the bike would not run the guy tried for over an hour to get the bike to fire off he tried jumping it off with his car he told me the bike only needed a carberator. The bike finely fired off with some starting fluid.  He told me the bike needs a decompression solid was bad on this bike and that I could weld a handle on it and use it manually.  I got the bike home bought a new battery  cleaned the carb. Notice the needle value was up side down I fixed it the bike fired right up and ran good I drove it all over town. The next day the starter was sticking I cleaned the starter and no luck I ordered a rebuild kit from eBay and it was the wrong one it made the starter run backwards.  I took the new kit milled it down sauterd it on the old part and it worked fine. This bike starter button does not work it has a toggle switch to start the bike under the seat. Also the horn button does not work.  The kick stand kill switch has been bypassed, the clutch switch has a jumper wire on it.  I rode it to work 65 miles one way. Got off of work battery was dead. Jumped it off I got half way home and the bike died like it ran out of gas is what it acted like and the battery was dead. I charged the battery back up and bought a solar charger and drove it back to work bike dose fine going to work with fully charged battery. After work battery tried to crank the bike so I got jumped off again riding home the head plug started leaking very badly I had an extra quart of oil with me the bike died like it was out of gas I noticed it was low on oil it had leaked all over my boot. I replaced the oil thought it might have a low oil kill switch.  The battery was dead.  My girl friend jumped me off was riding home got pulled over by the cops running bike with no lights 1000 yards from my home when it was getting dark my girlfriend was behind me with her emergency flashers on. They let me go with just a warning.  I had a guy look at the bike it  had two wires touching on the starter really I did not know about he thought that might have drained the battery.  He told me it needed a voltage regulator.  I fixed the head plug leak  and the two wires that where touching.  Waited on my voltage regulator I bought used off of eBay to come in. Bike ran good all over town. So I decided to try to save some gas money and take it back on the 65 mile ride to work and broke down 15 miles from work. One of my coworkers took me to work. After work they jumped me off the bike died on me again 25 miles from the house I tried to bump start it going down the road but no luck before the bike slowed down I tried to push start the bike but no luck.  Left me walking 5 miles to get cell phone service to call for help.   :'(  Now the battery is fully charged the bike fired right up. Only thing I noticed different is this time getting jumped off the bike had light with the new voltage regulator  the old one did not.

Wow!! That bike has been a real nightmare. What a project. Of course it is 27 years old. I would forget about driving it to work till you get all the kinks worked out. Guess you could disconnect the negative side of the battery when you get to work and reconnect when you get ready to leave work, at least till you find what is draining the battery. Fully charged battery should be 12.6 volts 2.1 volts per cell so with it running it needs to be charging at something greater than 12.6 volts. I don't remember where the rectifier bridge is on this bike but if one of the diodes is shorted it will affect your charging voltage as well. It converts from ac voltage to DC voltage.