I have been downloading a game(560mb) and it reached 99% and I received an error stating it can't continue and it would have to reset. I made copies of the the file as it was downloading incase something like this would happen. The last part file I have is 540mb.
How can I get the downloader to continue from that part file so I don't have to start again? Where does the GOG Download store this information?
I have waited around 8hrs for the download to finish and I don't have a lot of net to waste so this is really annoying.
Thanks.

afaik there is no way to continue from a partial file
you will want to try downloading the game again, only pausing part of the way through.
it has been known to work in the past and I believe it will work with this.

Download location can be set from within the downloader.
Unfortunately, the GOG downloader refuses to recognise a partially downloaded file from an earlier point.

How does the pausing help?

Pausing causes the connection to be dropped. Resuming fires off an entirely new request, so each connection is in use for a shorter period of time, which might help... although I have to say it's not very likely.
I'm not sure how the downloader works... if the files are identical to the ones you can download via the browser and if the downloader doesn't initially create zero-padded files (i.e. if the file "grows" as you download), then you might have some luck using something like FlashGot+FreeDownloadManager, which can resume from existing partial files.

I understand that as well, but I myself have had these same kind of issues, and pausing fixed it (this was with Fallout Tactics).
Another thing to try, is if you have spysweeper, disabling that, or any other security software before downloading, should help as well.

I personally haven't even seen a GOG downloader. I just downloaded games from my account page and I had no problem.

Same here. Firefox has handled everything beautifully so far and the transfer rate is so high that I haven't even bothered handling this to FreeDownloadManager yet.

I use Firefox as well for my downloading purposes. The downloader works just fine.

/* OFFTOPIC
The whole browser works damn fine and although I'm a little disappointed that the new Ctrl+Tab interface was disabled for 3.1, the current betas are still definitely the best browser I've seen so far, both for speed/memory efficiency, but also features/extendability.
*/

Each time I try to pause and resume the download, it fails to re-connect. This occurs with both the downloader and browser.
I'm trying the FlashGot+Free Download Manager solution, but I don't think it will work because the downloads are probably on sessions.

What is your primary browser??

It's Firefox. I'm now trying the download with Free Download Manager however if I attempt to pause the download and start it again, it fails because of an invalid username and password(but as you know this password would be for the server).
So the only way to download is to never pause and leave the PC running and hope nothing happens. Pretty lame...

Try this instead:
Go to your account and download the game from there using the Firefox downloader and see if that helps. I don't use anything but that and I haven't had any problems.