Are you sure that the .part file was removed ?

Note that you shouldn't restart such an interrupted download without keeping a backup of the .part and final destination file with size 0 bytes.

The usual procedure where you want to resume an interrupted download is as follows: Make sure to backup the .part file and the final file with size 0 without the .part before starting Firefox. Try these steps to resume an unfinished download if you still have the .part file.

1. Move the old .part partial download and the final file without the .part that has size 0 to another location.
2. Start a new download and pause it, don't close Firefox.
3. Copy the two files (.part and 0 byte final) that you moved above back to the download location to replace the new files that were created.
4. Resume the download in Firefox.

Yes, I'm pretty sure it was deleted. I found this procedure in some other support thread, this is how it all actually went.

1. I started the download, but I didn't realize I was on a free VPN with limited data amount, so I ran out of it and the file stopped growing, but firefox was still attempting to download.
2. I made a copy of the .part file to other location
3. soon after I finished copying the part file, Firefox realized it's not downloading and stopped. the .part file was deleted, but I had the backup
4. I found the solution you suggest and followed steps 2-4. It worked, firefox continued download
5. network got interrupted again - the laptop was suspended by accident, and when I woke it up and unlocked it, Firefox stopped downloading after cca. 5 seconds and the files were gone

You didn't kept the .part backup from the previous time, so you could retry a second time ?

Note best is to pause the download if you notice network issues because if Firefox times out then the risk is higher to lose the .part file.

same thing happens to me i want the part files to stop disappearing because then i can restart the download but the files keep keep getting deleted which is really annoying have u found a solution?

No, I haven't found a solution with Firefox. I ended up downloading it using wget

I am having the same problem where a download is interrupted due to network issues or the computer going to sleep. the .part file only appears for a moment in my downloads folder on the hard drive when im back online, it disappears before i have a chance to copy it. very irritating!