HTTP downloads stop after some time, resuming is not possible

Even more strange: when I resume the download that hanged over HTTP using FTP or HTTPS, download a few bytes that way, stop wget and then resume again using HTTP, it loads data again! But after a few MB, it may stop again. Unfortunately, files downloaded that way are always broken (the MD5 sum is not correct)

This screams "broken proxy" The protocol for resuming an HTTP download is not in any way complicated(it's just an extra header), but this is exactly the kind of thing that a broken proxy would be messing up.

I bet if you try to download a big file using wget, wait for it to fail, and then run wget -c changing http to https, it will resume just fine.