93 Camaro just shutting off.. wtf!?

Alright guys, I came here before talking to anyone else, because i know you'll have an answer.. or at least some ideas. My 93 (3.4L) is being all sorts of un-reliable lately. I'll be driving and she'll run fine... Then every once in awhile, I'll start it up, drive about a mile and she just quits running. Everything else works (radio, headlights, etc..) just stops running while in drive and going down the road. The car usually won't turn right over right away, but after a couple minutes will fire up and drive without a problem.. Hoping this is just something simple, or it may be time to finally let her go. I've been hearing a low pitch whine coming from under the hood intermittently for the last couple weeks.. It's been suggested that my alternator may be going bad.. It was rebuilt about 5 years ago at a local shop, so it wouldn't surprise me.. sound possible?

Marcus

Any codes? Use gage and check fuel pressure? When it refuses to restart, have a helper crank it, while you check for spark at the plugs and injector pulse. If you have neither one, check for an rpm signal. How long since a tune-up?

sorry i didn't see this earlier marcus. when you say it won't turn over until after a while, you mean if you turn the key the starter won't even crank?