You don't mention anything about a possible blocked gas cap vent.

as it attempts to die press the primer button to see if you can keep it running.....if it remains running I think you low speed jet may have an obstruction that is intermittent....does it ever die when you are under a load?

A point to mention on the fuel line. Too much isn't a good thing on these. A slight bow in the line is ok- but too long of a line can create a situation similar to a vapor lock. Good advice above. If you can confirm it is a fuel problem- you are 1/2 way there. Also , if you had removed the main nozzel- it is best to replace the seals.

@tomplum -- thank you for mentioning that. When I replaced the fuel line, I just cut it to the same length as the old one. But then when looking at it after the reinstall, I realized it had a dip in it and wondered if that might cause difficulty. I'll go back a snip a bit more off so the fuel never has to run uphill.

This theory is actually pretty relevant, as the previous owner complained that the mower "wouldn't stay running" for her. I thought I'd found the problem when I removed the carb bowl and discovered a bunch of mushy crud in there, but maybe that wasn't what was really causing the stalling.

Well, I shortened the fuel line just slightly so it's running entirely downhill. Recleaned carburetor, this time with a WaterPick (the kind you use to clean your teeth that shoots little jets of water -- my new favorite carb cleaning method, because you don't have to fear spraying carb cleaner in your eye and can watch whether the water's come out well or not). Unbent a staple and recleaned the holes in the carb bolt.

In the process of disassembling and reassembling, I discovered that one of the screws holding the air filter housing had a flat tip, while the other had a cone-shaped tip. It struck me as odd that the flat-ended one was in the hole that had gas and air passing through it, so I reversed them and put the cone-shaped one in the hole that had gas and air going through it.

Somewhere along the line, I seem to have solved the problem, because I cut grass with the mower for about 20 minutes and it ran fine. So thanks for all the tips.

Now my only concerns are: 1) my ear senses that the mower seems to be running a bit fast, and 2) the mower is definitely very loud compared to other mowers (muffler dosen't have any obvious external defects or holes). For what it's worth, the exhaust air seems to be blowing out of the muffler with tremendous force -- none of my other mowers make flowers, etc. flap in the breeze like this one does. Thoughts?

maybe the internal baffle of the muffler let loose. i like the water pic idea though.