You cannot perform backup/synchronize mail settings or calculate statistics. Try to manually launch mchk.exe, statistics.exe or see Event Viewer in regards to Scheduled Plesk tasks. You will see errors like:
SOAP failed. Failed in sending message at (SmarterMail::checkResult line 175) at execute console command --all-domains(vconsoleapp::start line 129) at execute mchk.exe --all-domains(vconsoleapp::run line 140)
Check that SmarterMail password in Plesk is the same as in SmarterMail installed on server. If it is not, set SmarterMail password in Plesk according to admin password in SmarterMail.
For SmarterMail 9.x:
Delete the SmarterMail site from IIS and reconfigure it to use SM Web Server. The procedure of reconfiguring the site to use IIS instead of SM Web Server is described in SmarterMail documentation. I.e. the actions opposite to the described ones should be done.
For other versions:
Reconfigure SmarterMail to use IIS webserver instead of SM Web Server. The way of reconfiguration is described in SmarterMail documentation.