We solved the issue: we had an expired certificate on the server. Upon renewing, we were able to configure the client.
Confusing was the fact that we configure CRM client to connect to "http" address, not to "https". But in the log located in C:\Users\name\AppData\Local\Microsoft\MSCRM\Logs\Crm50ClientConfig there was an error "Metadata contains a reference that cannot be resolved: 'https://..." That gave us a clue about certificate...
Good luck to everyone who has a similar issue.
Lana