Have done a search and found a handful of threads for this similar issue but nothing all too conclusive on a solution, but I have a hunch and wondering if anyone else has had this issue and fixed it.
I have a high mileage 07 Denali (195k) and about 3 months ago at the tail end of a long day of driving it bogged down and stalled while on on the highway. I was able to pull it off the road and tried to restart but it would not stay running. Would fire up, idle rough for about 5 seconds, then stall. I thought it might be an oil pressure issue as the piston rings are worn and it burns a lot of oil. Called a buddy to bring me a couple quarts to see if that would get her running. After waiting for about 45 minutes my buddy showed up, I dumped some oil in it, and it it fired it up and ran fine. Drove it back home and hadn't experienced the problem again until a couple months later. Was driving back from an event and same thing - this time it stalled while in stop and go heavy traffic on the highway. Was able to limp it off the road and into a gas station. I put a bunch of oil in it again right away but that did not fix it this time. Still rough idle when starting then stalls soon after. Had it towed home and replaced the battery as it was old. Next day it started fine and had been running fine since the other day.
Had the same issue just a few days ago sitting in a parking lot letting it idle for a while. Was waiting for someone in a grocery store and wanted to have the AC on because it was hot so I was sitting with it running for a while. Started to bog down just sitting in the parking lot so I shut it off. Had the exact same issue... rough idle/stalling at low RPM didn't want to stay running. Let it sit overnight and next day drove it home fine.
Now here's the nuts and bolts:
It has two relevant codes - Fuel pump relay, and Catalytic Converter. The fuel relay I'm actually pretty sure is NOT the issue as this popped up only because I removed the relay when doing a wet and dry compression test on the motor. I bought a new fuel pump but have NOT installed it yet as I don't think that is the issue - as the problem is not consistent with a bad pump. Wouldn't make sense that the pump would only have issue when running for a long time, and would magically work after it sits for a while.
Here's my big question: could the cats be causing this?
As I mentioned my truck burns a LOT of oil. This has likely ruined the catalytic converters (which is why they are throwing codes) and since this rough idle/stalling issue only happens when the truck has been running for an extended period of time, I'm wondering if the cats are clogging up the exhaust when they get hot. Thoughts? Anyone else experience these same symptoms?
