After hours of testing I found out, that
- when the error occurs, deinstalling the C400 device driver and reinstalling it makes it work again,
- when the error occurs, not only Pro Tools SE can't recognize the device, but Steinbergs Cubase Elements (which I installed as demo version) doesn't do as well (so it's a device driver problem, not a problem with Pro Tools SE),
- the error corresponds with using different USB ports for connection. I can't exactly reproduce the error, but whenever it occurs, I used a different USB port. I couldn't find out, whether it's a specific port, the number of different ports I used or the order in which I used them. And I won't spend time on finding out but will start recording now
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So thanks Routingwithin for your assistance.