"Could not initialize the application's security component."

Have you updated your virus/security software lately? Perhaps it's causing a conflict. Even if you haven't updated it recently, changes in version to portable apps may be triggering your security software where they didn't in the past.

Or maybe the problem is even simpler than that... you have a virus. Not trying to pass the buck here but lots of us are using FirefoxPortable without issue, so there something in particular with your system setup/configuration that is causing a problem.

Oh and as John suggested, trying to run FirefoxPortable from your local hard drive will confirm or deny problems with either your flash drive or your PC depending on what happens.

You may consider it comical, but I've seen it dozens of times. Even the name brand drives are often using lower-quality components these days. They're optimized for individual large files, NOT lots of small files. OpenOffice.org Portable alone, for example, has about 4,300 individual files within it. It doesn't matter how full your drive is, it matters how much of a workout you give it.

A simple check is always to install an app on your hard drive, say C:\PortableApps\FirefoxPortable and run it. Make sure it works properly and is happy. Then copy it to your device at X:\PortableApps\FirefoxPortable. If it then starts having issues, it is 99.9% sure it is a hardware problem: either the device itself or issues with the PCs USB ports.

I say again that the errors you see simply can not be caused by the simple act of installing software or copying files. We work with several large flashdrive makers and know the ins and outs of the hardware and firmware. And we've got 5+ million users worldwide and growing every week. I'm not pulling these ideas out of thin air. I'm basing it on what we know, what we've seen before and what we've learned as the longest-running and largest portable software organization.