file was too large so I deleted it. I then created a new file with the same name and permissions:
chown root:utmp /var/log/btmp
chmod 600 /var/log/btmp
The problem is that now new items are NOT logged.
btmp begins Mon Nov 18 06:38:03 2013
I use CentOS.
I found this link, demonstrating that I am not the only one to experiance this problem: