To the best of my memory, most of the outages have seemed to be during late night/early morning hours in the U.S. Central time zone, but this isn't a terribly large sample size.
Similar 1-minute downtimes seem to happen once in a while at other times too, but I haven't noticed specific times yet.
If it is a backup script kicking off, there should probably be a throttle on it, whether it is causing the db to run out of connections, or just the bandwidth to be used up I don't know.