I have a bunch of small LED flashlights that use three AAA batteries in a holder that gets inserted into the body. They cost a little over a dollar a piece from Amazon.

I did a load of laundry yesterday, and when I opened the lid of the washer, I saw a light! I had left one of those little flashlights in a pocket, and the washing machine turned it on. It went through the 43 minute cycle, and it still works. I took it apart to dry it out, and my cheap little light is bright and healthy. Surprising, especially with the electronics of the LED.

As I said earlier most small LED torches fail because of the lack of a conductor through the screw thread where you change the battery (there are other failure modes too but I have found this is the predominant one). I'll talk about them below. To fix the screw thread point I have found the easiest way is to scrape the anodising off the flat part of the ends of the threaded section, then carefully run a steel brush around the threads themselves. The idea is to try and remove as much of the anodised layer as possible. You don't need much to come off as long as you have matching points since this is one of the electrical paths between the switch end and the LED. Then I add some deoxit to the threads. This is usually a reasonably good fix.
Another failure point can be where the bit threads into the end where the switch is - sometimes you need to reposition this to make contact. A bit fiddly though. And the last point is where the body joins the LED carrier pcb. Sometimes this is just a blob of solder and it doesn't made a good connection here. I dismantle if possible and increase the size of the solder blob a wee bit. Deoxit this also.
I have had switch failures but rare. Also had the odd failure of the LED/pcb also rare.
The issue is basically very poor design and manufacture and shouldn't happen. Probably why these torches are so cheap. You think that perhaps 50c extra spent (and that is all it would take) would be well worth it and you would be quite happy to pay the extra as well for a working torch. Unfortunately a Chinese manufacturer doesn't think like that so a few cents saved makes him more money since we keep on buying the things. They also think that if their torch is 10c dearer to buy compared with a competitor that he won't make any sales because you will always buy the cheapest. Do a google search on 'tofu buildings' if you want to see an eye opener.
Generally 'brand name' torches will be dearer and much more reliable.

Thanks for this info. I've been very happy with the cheap three-battery lights. I have them all over the house. A couple failed because of corrosion on the contacts of the battery holder. Once I cleaned them, they were back in action. It's the fancier single-battery lights that have been unreliable. I like the three light levels and the adjustable beam, but if they don't work, those features don't matter.

I read reviews on Amazon before I buy, and if the one-star reviews are over 15%, I keep looking. I also read the reviews to see why people gave them one star. Sometimes, it was the wrong color, or the box was damaged, or some other irrelevant reason. Unfortunately, I'm not allowed to post on Amazon any more. I was banned for violating their policies, but they can't expand on that. I had hundreds of reviews on Amazon, and they were all removed. Each one was reviewed before it was posted, so I don't know what they think I did wrong.