Is it possible for the sound card to fall out?

It is possible, although unlikely if it was installed correctly. It would be much more likely in a desktop system, but I don't know what kind of computer you are using.
If you are using a desktop computer, opening the case to the system is usually simple and it wouldn't take more than a glance around the components to see if the card has fallen out.
A laptop would be a more difficult situation, but still do-able if you know what you are doing. I, myself, would not mess around with a laptop's interior, however.