I'd talk to your webhost if you're concerned. This is the connection to your MySQL database which is the backend of Wordpress.
Mine was having a ton of connection issues every few minutes this past weekend, and after going back and forth with my webhost I think what happened was that my backing up all my files using FTP triggered an alarm, and they semi-blocked my IP until they figured out if the activity was safe (they have now white-listed my IP). I kept telling them I was getting this error and they said it looked fine when they tried it! Do you have some sort of backup or other activity happening during those hours?