Yeah, use the cut-off switch on the negative side...safer that way. Seems to be less of a spark when attaching to the neg. side than the pos side.
Hope that turns out to be your problem.
I remembered, we were at the State Fair a couple of years ago...(we do a club display every year). Come time to go, and the "Apple" don't start...no click, no nuttin...
I didn't have my booster box with us that day, so I get someone else that has cables, hook them up, and still nuttin.
Turns out MY disconnect was corroded just enough to keep it from making contact! Took it off, cleaned it quickly, and it worked fine. Once I got home, I cleaned it mo better, and it's been good since then. It's them danged stoopid things that'll git ya every time!

Had a similar problem with my 77.  It ended up that my starter and/or the solenoid was overheating due to having headers on the car.  I used racing heat wrap around both of them to reduce heat off the headers and have had no problems since.  Hope this helps!

[QUOTE=Adams' Apple]...Sounds like...a solenoid heat soak issue...[/QUOTE]