Hi Anastasiia,
I had the same problem (and was not able to find any information in the log files) in a dashobard with DS 1.6 SP1 and this was definitely no time-out issue. This error ocurred, when opening the dashboard from an open-Document link.
When I opened the webtemplate from the BI launchpad, I got a specific error message (from the underlying BW system) with a lot more information than the unspecific "application does not exist" message.
Perhaps you can give it a try.
Best regards,
Michael