Engine starts and then stalls while driving?

Let's start with the P0171 and p0300 code's I need to know if you have the hybrid engine or the regular 5.3 engine?Iam thinking since you replaced the intake gasket gasket and ran good for a little while you could have a warped intake manifold. Let me know what you have.

Also does it run any better from when it's cold to when it's hot?

If the engine has a vacuum leak for instance and the rpm is unsteady from that then yes the throttle plate would bounce around. Because the throttle plate move's to adjust the idle so it's try to adjust the idle and can't because of the poor way it's running. So how were you trying to check for vacuum leaks?The best way is to spray carb spray around the intake manifold gasket vacuum line's etc and watch for a rpm increase decrease or the engine die's out. If you have a scan tool that will read live engine data then take the scan tool hook it up to the truck select live engine data and watch the fuel trim while your spraying you will get a spike on the fuel trim if the engine suck's any carb spray in. Let me know what you find.

Have you tried taping on the mass airflow sensor lightly with a screwdriver handle to see if it die's or run's any different?The fuel pressure spec's are 385-425 kPa (55-62 psi) let me know what you find.

Before we change the intake manifold let's check some other thing's especially since you couldn't find a vacuum leak by spraying carb spray. Try this let the idle then unplug a injector and see if the rpm's drop then plug it back in and go to the next injector and make a note if any cause the rpm's to drop and which one's do. Also do you have a scan tool that could tell you which cylinder's are miss firing and that can read live engine data that would really help. Let me know what you find.

Here is some info you can use.
Bulletin No: 05-06-04-029A

Date: June 24, 2005

TECHNICAL
Subject:
Flexible Fuel (RPO L59) Rough Idle, Misfire, MIL DTC P0300
(Install Intake Manifold Gaskets With Teal Green Gasket Material)

Models:
2002-2004 Chevrolet Silverado, Suburban, Tahoe
2002-2004 GMC Sierra, Yukon, Yukon XL
with 5.3L Engine and Flexible Fuel (VIN Z - RPO L59)

This bulletin may apply to the following engines using regular fuel: 4.8L, 5.3L, 6.0L (VINs V, T, P, U, N - RPOs LR4, LM7, LM4, LQ4, LQ9).

Supercede:

This bulletin is being revised to add additional diagnostic information. Please discard Corporate Bulletin Number 05-06-04-029 (Section 06 - Engine/Propulsion System).
Important :Always begin your diagnosis with the Diagnostic System Check - Engine Controls (SI Document ID # 1289827) for any MIL or driveability concern. The Diagnostic System Check directs you to the next logical step in your diagnosis. Follow the instructions in this bulletin should the rough idle, misfire, or DTC P0300 diagnostic procedure point to an air leak in the intake manifold gasket. Following the published diagnostic procedures will improve diagnostic accuracy and support our fix it right the first time approach.

Condition

Some customers may comment that the vehicle may have a rough idle, misfires and/or a MIL illuminated with a stored DTC P0300.

Cause

The L59 engine is calibrated for ethanol fuel (E85). Due to the low volatility of ethanol, the PCM provides higher fuel flow through the injector, which may pool on the upper manifold to head gasket material. Overtime (usually 12 months and longer), the gasket material may degrade resulting in an unmetered air leak.

Correction

Replace the upper intake manifold gaskets with the teal green gasket material, P/N 89017589.
Important :Do not replace the upper intake manifold gaskets with the original orange gasket material, P/N 17113557.

Inspect Intake Manifold to Cylinder head Deck for Warpage

Important :The intake plenum should also be checked for excessive warpage that may cause an uneven clamping pressure of the seal. If the plenum is found to be warped it will need to be replaced. Service Information states, "An intake manifold with warpage in excess of 3 mm (0.118 in) over a 200 mm (7.87 in) area should be replaced." Intake warpage is measured at the gasket sealing surfaces and should be measured within a 200 mm (7.87 in) area. This measurement is across only two of the intake runner port openings. Measurements taken across the entire distance of all four intake runner ports will lead to unnecessary manifold replacements.

Important :Measurements taken across the entire distance of all four intake runner ports will lead to unnecessary intake manifold replacements.

1. Locate a straight edge across the intake manifold cylinder head deck surface. Position the straight edge across two runner port openings.

2. Insert a feeler gauge between the intake manifold and the straight edge. An intake manifold with warpage in excess of 3 mm (0.118 in) over a 200 mm (7.87 in) area is warped and should be replaced. Do not replace intake manifolds with warpage that measures less than 3 mm (0.118 in) over a 200 mm (7.87 in).

Your welcome glad to hear you got the truck up and running again as far as the check engine light goes if you don't live in california I would take it to a auto part's store and have them clear the code's. The light will turn off by itself over time but I would have the code's cleared.

Do you have a check engine light or has flashed?

Get the idle air control valve and throttle position sensor checked out-ain't it comeback for the more complicated stuffs-

Clean the throttle-body and idle air system, where applicable. Any trouble codes?