I have a 1973 Duster with a 1968 318 engine. Here's my problem:

I set the timing according to specifications. I drive for a while then later when I try to restart the car, it won't start again until I have reset the timing. Once it is reset, it starts right up.

-I recently (as in a couple years ago) changed the timing chain
-The air gap for the distributor is in spec
-The engine block is a 1968 and is set for 1968 specs (this caused some frustration earlier)
-carburetor is new

Any additional suggestions from you guys on where to look for the source of this problem?

is the distrib clamp bolt tight? I cant think of anything besides this that would let the timing change.

I just checked it to be sure and it's tight..

Had an aspen w this problem. Several things I found- dist bushing had play, timing chain slack, slipping dampner, and worn cam. Every single time I drove it the timing had to be reset, so I got pissed and yanked the motor and replaced w refreshed one so I could drive car and diagnose engine out of the vehicle....got a spare laying around?

Also, every time I set the timing, it had to be set ahead, because once you tightened the clamp on the dist down, the timing mark would move. Actually watched it happen while friend tightened bolt.

Electronic ign conversion or are you meanin point gap?. If point gap next time (actually with either one) BEFORE you crank it see what the gap is & you might pull (& GROUND) the coil wire & crank it & see what the timing light shows for initial. Any possibiblity it ain't a timing issue & something else is causing this (heat soak etc). I would go over the dist innards from head to toe tho.

Is there any consistency in the amount of timing that is off? Is it retarded or advanced? Do you have to reset the timing no matter if the car is cold or still hot/warm? Last, have you ever checked the timing before you shut it off?

Is there any consistency in the amount of timing that is off?
Not that I can detect

Is it retarded or advanced?
The factory specification for 1968 is 10 degrees advanced. When the timing shifts after operation, it appears to be retarded. Because I have to advance it to put it back to spec.

Do you have to reset the timing no matter if the car is cold or still hot/warm?
The timing only shifts after it has been in operation, so warm.

Last, have you ever checked the timing before you shut it off?
I haven't tried that yet.

The car is electronic ignition. I've changed the cap and ordered a new distributor, hopefully this will help.

Vacuum disconnected when setting timing?

Check the gear on the distributor,is it tight?

gear on the distributor? There is no gear on a small block distributor, nor a big block for that matter. There is one on the slant 6 though.

If the gear on the intermediate shaft was loose, which is where the gear that drives the distributor is actually located, then the oil pump would be failing too. Has the OP seen oil pressure issues?

this deal ain't makin any sense, we're missing something here. I cant wait till we get to the bottom of whats going on

I stand corrected.
I should have stated distributor drive gear.
"it appears to be retarded. Because I have to advance it to put it back to spec.
This is with a timing light?How does it run when you start it with corrected timing and how long?
Distributor bolt is tight but is the distributor itself tight?

Good point, bolt could be bottoming out before the clamp tightens down on the distributor.

Other thing that's been floating in my head, and it's way out there, is a broken distributor shaft inside the housing.

If the shaft was broken I would bet it would be a whole lot worse,under acceleration or high rpm the timing would probably slip beyond runable.

Does your timing chain have all steel gears ? or the plastic coated ones ?

I've seen this happen once on a car where the intermediate shaft gear and the gear teeth on the cam were almost totally worn away.

Pull the distributor and look at the tang. Also pull the intermediate shaft and check for wear.

The vacuum is blocked when setting timing, so yes.

It is tight.