That's such a coincidence, because my Dad gave me a pair of his old cans a while back because they had exactly the same problem... It was a dry connection at the plug, as you might expect.
I left them lying around for months because I'm such a lazy bum, but in the end I ordered a new plug from some ebay dude, and got to it with a soldering iron. I daresay someone else could have done a better job, but it wasn't as delicate as I'd thought it might be.
The weirdest thing? Mine are Grado SR-80s as well! I'd never heard them in all their glory till I finally got around to fixing them. And wow, what a wonderful pair of headphones! Definitely worth getting 'em fixed.
If you think that the problem is with a connection at the plug, it's not hugely difficult to buy a replacement. If you do decide to try it yourself, or you buy the parts yourself, I'd recommend either of these:
Switchcraft 3.5mm Stereo Jack Plug Gold Plated Pro
NEUTRIK NYS231, 3.5mm stereo jack plug
I looked into it a bit at the time, and they were both highly recommended as replacements.
Also,
this set of videos shows someone rewiring almost every part of a pair of 60s, just in case you think the problem might be elsewhere...
QW