@Pawel: The PI OPC DA/HDA Server utilizes the PI SDK library to communicate with the PI Server. It can be affected by network latency or firewalls.
Can you increate the connection timeout for your PI SDK connections? You can perform this with the PI SDK Utility tool. By default, this is set to 10 seconds, you could use 60 seconds and retry. Is it only the browsing capability that does not work? Do you succeed to read a given PI Point value such as \\server\sinusoid you manually type it?
I am facing a similar situation where i installed PI OPC DA/HDA 2010 which has SDK 32 bit (PI SDK 18.104.22.1688 )and PI Web Services 2012 which has SDK 64 bit (PI SDK 2012) on same server. The OPC was working but as soon as i install PI Web services it fails where as web services works fine. I intend to downgrade my PI Web services to 2010 32 bit version. Is this the correct method?