What exactly means "gone"; from Control Panel, from the install folder C:\WINDOWS\system32\Macromed\Flash, from the IE add-ons?
it has gone from IE. When I browse youtube or sth. like that, the page tells me to install the flash player. A look in the control panel > programms tells something different: here I can find the one for IE and the one for FF. The folder you mentioned seems to be ok - it is not empty (screenshot).
In IE under Add ons, there is Shockwave Flash Object active but only when I switch to all Add ons. In IE internet options the rendering is set to software instead of GPU.
So why does Flash only work when it is installed, but after a reboot, youtube tells me to install flash?
I found an old topic that describes the same symptoms as you see. The resolution then was to check the Permissions for each file in the C:\Windows\System32\Macromed\Flash and C:\Windows\Syswow64\Macromed\Flash folders, and make sure that at least Read & Execute is allowed for every user. (Right-click on each file, Properties, Security tab.)