thank you for answering pretty fast. Yes, I know all that about rain and weather. Now it is good weather and the Rx SNR is over 10 again.
What interests me most is, if the company offering the sat-service could eventually kick me out of the contract due to a low Rx SNR. The speed of the connection is acceptable, even with heavy rain. Only the Rx SNR is very poor. And I do not want to loose the contract because of poor weather.
It should manage below 10. I've used Ka band satellite services much lower than that, although on Avanti not Eutelsat.
If it goes too low you will of course lose connection, but if you're not, it sounds like you're ok. I would imagine you have been told they will kick you off the network (e.g. the modem has to renegotiate back in to network), not they will terminate your service.
That said, satellite companies have to be careful, if your dish is slightly mis-pointed it could be hitting another bird, and your Tx power will have to go up significantly to cope. It may need to run at a lower QAM level because of your poor SNR, which means you would take up a larger timeslot for the same bandwidth, which they may not like.
But, it's likely either due to water ingress on the cable/connectors, which would be the fault of the installer, dish misalignment, which would also be the fault of the installer not properly tightening it or aligning it, or a tree/whatever in the way.
As long as it's not the last one, your ISP should be able to send an engineer for you.