I think the process is running in kernal mode http://cloanto.com/kb/14-139
In that case, could you please try running the following from cmd as administrator to generate the dump file? Replace SVC_PID with the real AvastSvc PID (5272 in the last screenshot).
It will create, run and delete a task that uses Avast dump system.
@schtasks.exe /CREATE /SC ONIDLE /I 999 /RU "NT AUTHORITY\SYSTEM" /TN "SvcDumper" /TR "\"c:\Program Files\AVAST Software\Avast\avdump.exe\" --pid SVC_PID --exception_ptr 0 --thread_id 0 --dump_level 1 --dump_file c:\service.dmp"
@schtasks.exe /RUN /TN "SvcDumper"
@timeout 10
At this point, please check that the scheduled task has really run. If the file "c:\service.dmp" was not generated, run Windows Task Scheduler, look up the created "SvcDump" task, right-click it and select run (shown in attached screenshot).
The last command deletes the task.
@schtasks.exe /DELETE /TN "SvcDumper" /F