Are you sure those files are actually being deleted? Maybe the downloads history is set to be cleared?

Tools > Options > Privacy = History - Use custom settings for history

Then look at the pref for Remember down load history (needs a check-mark) and Clear history when Firefox closes (un-checked) unless you want specific items to be cleared on shut-down - then hit the Setting button and de-select that Download History item.

I think the latter may be check-marked - privacy.sanitize.sanitizeOnShutdown - is set in your preferences.

yes the downloads are actually being deleted. I've actually had the downloads folder open where I save everything too and watch it actually delete when firefox closes. right now the only way I can prevent something from being deleted is either rename the file or make a copy of it. remember download history was checked, and clear history was un-checked. so that's not the issue.

It is possible that an extension or security software is deleting the files.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of your add-ons is causing your problem (switch to the DEFAULT theme: Tools > Add-ons > Themes).

See Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems and Troubleshoot issues with plugins like Flash or Java to fix common Firefox problems

You can also uninstall the Java Console extensions that show in your plugins list.
See http://kb.mozillazine.org/Java#Multiple_Java_Console_extensions

ran firefox in safe mode, same results. download got deleted. downloaded ok, virus scan completed with no issues. but as soon as I close firefox. file deletes. I'm convinced this an issue in 3.6.10, didn't have this issue in any of the older versions. and file extension type doesn't matter. downloaded .exe, .pdf, .zip, .rar, .txt, .msi, etc. etc. all get deleted.