What causes a bicycle tube to leak where the metal meets the rubber on a Schrader valve stem? I've had three tubes fail the same way over the past year. I make sure the stems are perpendicular to the rim. I'm not sure what else to check for.
Does this joint have a name?
Am I correct that there really isn't a good way to patch/fix this type of leak?
It is unlikely that the leak is coming from that spot, as David said that is a solid tube of metal. You could be feeling air escaping there due to either a poorly seated/loose valve core, or sometimes your leak is from the tube, maybe a pinch flat, and the air is escaping from the gap between the stem and the rim which makes it seem like the stem is leaking. Do as Hursey suggests and inspect your rim, but also look for and feel (carefully) around the entire inside of the rim for jagged and sharp spots, also inspect the inside of the tire for sharp objects that could be puncturing your tubes. sometimes even wire fragments from the tire casing itself can break free and put a hole in your tube. If you have a valve core tool maybe check that its firmly seated.
Do you have access to a valve stem tool?
Could be the valve itself was loose in the stem, and air coming out there could have felt similar to a leak up the sides between the brass and rubber of the stem itself.
If the valve hole in the rim is ragged at all, it can slowly cut a hole in the tube. Swarf from drilling can be removed with a file or even a strong knife/scraper. Ideally you want that transition to be "soft" Also its okay for the rim-tape inside to overlap the hole's edges some.
You can get other styles of tube that have more metal and less rubber in that part of the stem. Some brands like schwalbe are even threaded like presta valves and have a similar retention nut.
As for the existing tube - you could try inflating it to about 5 psi ("firmish") outside of the tyre, then dunk the whole area in a bucket or basin of clean water.
The leak will show itself in a stream of little bubbles. By rotating the tube you can identify the exact source. If the air is leaking between brass and rubber then epoxy might help, but may not adhere to the butyl rubber. Possibly wrapping the stem with a couple of loops of wire then twisting them off may help, but I'd test overnight before relying on such a fix.
Otherwise, replace with another brand of tube.