checkdns.com says that:

2 DNS servers are online, but the third:

Error fetching SOA from ns3.mydnsserver.com

So, if only 1 of 3 DNS servers have some problem, why the domain can not be resolved?

Spain has a whois server. It is available via the web interface on www.nic.es [nic.es]. For some reason they don't provide a national whois service on port 4321 which can be queried from command line tools and remote processes though.

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Some 60% of them can open the website with problematic domain name but the others return errors something like "name lookup timed out"

2 DNS servers are online, but the third:
Error fetching SOA from ns3.mydnsserver.com
So, if only 1 of 3 DNS servers have some problem, why the domain can not be resolved?

I think you are close to the solution. The IP addresses of your three DNS servers are assigned on a round robin base to the visitor's browsers. There is a chance of 1 in 3 that they will get the wrongly configured DNS server assigned. This matches with your test that about 60% of your proxy tests succeed but the other 40% fail.
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Lammert, thank you for your reply.

So far I was thinking that if one DNS server is down, the request will be forwarded to the next DNS server.