Where are export files stored?

I can confirm that the "List Upload Status" option is supposed to show you the status window with a link to the last exported file for that list. This is even true if you've logged out in between. Each list has its own status window. 

Generally, we recommend to keep export files below 100,000 records, so there is a chance that your 120k export file errored out. Try splitting it up in 2 exports. Also, if you choose "all columns" your export will take a lot longer, so it is recommended to add all columns to your list view. 

I don't believe Marketo saves a history of past exports.  I know there have been ideas posted on there that range from some sort of list export archive to having an alert sent to the users email that is requesting the list export that provides a download link, similar to how list imports currently allow.

Kim - If the list was still exporting when Ben signed out of Marketo, then the file would not have downloaded anywhere.  When you export a list you have to click the Download Now button to initiate the download upon export completion.

Ben - I think if you select Show Export Status it should show a window in the top right of your browser window and if it is down exporting there will be a Download Now link available.

The report has finished exporting because when you check the export status, there is no pending export.

Here's a clarification:

Yesterday morning I ran an export of over 120,000 leads. Its started from 7:00 am and by 5:00 pm, it still wasn't done. I decided to let it run overnight. When I came in this morning, there was no more status bar, but the prompt to download wasn't there. Unfortunately, Marketo isn't intuitive enough to auto-download an export. Typically, in previous, smaller exports I get a prompt after processing that asks me to download. I got no such prompt in this one. Maybe my computer went to sleep, but I thought the export process was done remotely in the cloud and not locally so my sleeping computer shouldn't matter right? Where in the cloud does Marketo save that export that completed last night?

I ended up running the export process this morning again, but that previous export file could not have just disappeared in the ether somewhere...

Maybe look in your downloads (in whatever browser you were using) and see if it's there?

I have a feeling that your list is still exporting.  What happens when you clcik Show Export Status? 

It does not. It only shows
 
Show Export Status
Export List
Close Smart List
Delete List

You should be able to go back to the list that you were exporting, and then under List Actions there will be an option to show export history.  That should allow you to download the file if it has finished exporting.