Which version of rsyslog are you using?
Has the state file been successfully created and updated?
Are there other custom configuration snippets in /etc/rsyslog.d/?
It could also be a side effect of having $InputFilePollInterval and $InputFilePersistStateInterval 1 with the same value (1 second), try setting $InputFilePersistStateInterval to a higher value (5 seconds sounds like a good compromise).