The LT-1 350 (5.7L) engine (That is in your SS) has what is called an "Opti-spark" Distributor, this is a very common failure on this engine and will produce the same symptoms that you are describing!
To Test:
First, verify the "Security" light is not on or flashing in the instrument panel.
Next, Check for 12 volts to the ignition coil, Pink/Black wire, with the engine cranking.
Connect a test light to B+ (positive terminal) touch the White/Black wire at the ignition coil, Should have a blinking test light with engine cranking.
NOTE: This is not a fuel related problem, you are losing spark!
since it seems to happen at certain angles, it could be water (or other crud) at the bottom of the tank being sucked into the fuel line.
Perhaps a failing fuel pump. My experience is limited to a Toyota pick up truck that had done a similar thing. When you applied more throttle the opposite would result and a loss of power occurred. This continually progressed to the point that I had to nurse it so much that I could barely apply any power before it would shudder and attempt to cut off.
My other guess would be a clogged fuel filter.
Now if you are saying the "starter" wouldn't turn the engine over after going to eat, then you would be looking at a charging issue on the battery. If the alternator is not charging the battery, the car may start fine after sitting for a long period of time, (after the battery stabilizes) but eventually will loose power and not be able to provide a good spark to the engine. A way to test this is to start the car, and turn on the headlights. After a minute or so switch to the high beam setting and listen for a drop in engine rpm. Let it run that way for a couple of minutes. If you have an amp meter in the dash, the output should be around 14 Volts, usually the manufacturer marks the ideal amperage on the gauge, so it might just be in the "middle" area.
A local auto parts store can detect a bad charging system by hooking up a tester to the vehicle (for free). If the car is cranking slowly, then start there and have them run a diagnostic to check the battery and alternator. Otherwise, consider the fuel pump or fuel filter.
Good luck!
Sounds like fuel starvation due to possible vapour lock or restriction.
Check fuel filter . Pump and pressure. Check fuel cap etc and vapour canister and connections if fitted.
As it occurred going up an incline.. Did we have low fuel level ? Use more throttle etc both may affect fuel flow eg restricted..
May be worth having a scan run.
take it to the shop
Its a Chevy
I have a 1995 Impala SS, it only has 77,300 miles on it if that matters. Recently I was driving at about 50mph getting onto a bridge at a moderate incline. My car slowly lost power stalled and took about 10 minutes of me trying to turn it over until it actually started back up and I could make it over the bridge. I took it to a shop and they said since it wasn't doing it any longer they couldn't do much and I picked it up two days later. Going back over the bridge (uphill again) same thing happened. Two weeks prior I parked on a flat road and went to eat when I came back my car wouldn't start it took several times of me trying to turn it over again. And idea or advice would be appreciated!