When you get this error

Problem with internal logger. Please check the permissions on the /var/log/clamav/clamav.log file.

and

Mar 31 06:44:18 mail amavis[21634]:ClamAV-clamd av-scanner FAILED: Too many retries to talk to /var/run/clamav/clamd.ctl (Can't connect to
Mar 31 06:44:18 mail amavis[21634]: (21634-02) (!!) WARN: all primary virus scanners failed, considering backups

it means that clamAV is running under another user ( usualy amavis instead of clamav ) and log files have wrong permisions ( some of them may
have clamav as an owner ). They all should have read, write permisions for amavis user. Just simply change the permisions for the  
/var/log/clamAV folder by running

chmod -R amavis:amavis /var/log/clamav

Then restart amavis by running:
/etc/init.d/amavisd restart

It should solve the problem.