This works fine for me.

I loaded https://i.imgur.com/EiXtZYH.jpg and saved the image. The saved file was correct, and maintained its transparent background.

Note that the image above is actually a PNG.
For whatever reason, imgur serves it with a .jpg extension, so the saved file also has .jpg.

Perhaps when you are editing it you ended up converting it to an actual JPEG and thereby lost its transparency?

I've only tried downloading directly from Google images, and that's given
me a problem

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Can you give more specific repro steps?

I tried downloading some images off google images and it worked as expected.

I expect you are getting a different version of the image.

Are you using chromium, cause I'm using canary

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I have used both the current stable (69.0.3497.92) and the current canary (71.0.3552.2).

When using images.google.com in particular, I found that the initial thumbnails are a re-encoded JPG with a solid background. So if you download this, it will not be transparent.

However if you click on it, it then shows a larger version. If you save this image, it points to the original source image, and has the transparency as expected.

Given you are using the canary, you could be having issues from Network Service being enabled (can try turning it off using chrome://flags/#network-service), however it seems unlikely that would cause the symptoms you are describing.

Can you try disabling the network service as mentioned in comment #7 to see if that solves the problem and report back?

Going to close this, due to lack of followup (And suspecting this is a server issue - Chrome's network stack doesn't know how to re-encode an image, nor does the download code).