Is the Flash plugin file still there when that happens?

You can find the Flash plugin file NPSWF32.DLL here after you have run the Flash installer:

C:\Windows\SysWOW64\Macromed\Flash\

Do you have security software that may restore files or registry entries on a reboot?

Yes, the plugin file is still there. Also, I forgot to mention that this problem doesn't arise on other browsers IE or Chrome

IE uses a different ActiveX plugin and Google Chrome comes with its own build-in Flash plugin unless you've disabled it, so that doesn't apply.

If the plugin is there but Firefox doesn't find it then that would suggest that the registry key that Firefox scan to find plugins isn't there.

HKEY_LOCAL_MACHINE\Software\MozillaPlugins

I found a folder there named @adobe.com/FlashPlayer which contains REG_SZ files (Default), Description, Path, ProductName, Vendor, Version. It says I have the Flash Player 10.1.

Try to uninstall and reinstall Flash.

• http://kb2.adobe.com/cps/191/tn_19166.html#main_Uninstall_the_older_Flash_Player_version

You can use this link to download the latest Flash player and avoid getting any extras.

• http://fpdownload.adobe.com/get/flashplayer/current/install_flash_player.exe

The link you provided to reinstall Flash was dead. I tried uninstalling Flash as instructed and reinstalling it on the Adobe page http://get.adobe.com/flashplayer/ without the McAfee software and encountered the same problem as before; the Flash Player worked at first, but did not work after the computer restarted.

Download the Flash Player via this page: Troubleshoot Flash Player installation for Windows

• http://kb2.adobe.com/cps/191/tn_19166.html#main_Download_and_install_the_latest_Flash_Player_version

• http://fpdownload.macromedia.com/get/flashplayer/pdc/11.1.102.55/install_flash_player_32bit.exe

The first link you provided takes me to the same page I have been using. The second link's Flash Player does not work, as I am using a 64 bit system.