Might someone have multiple instances of down syndrome?

Yes...: The risk depends on the mechanism. Most Down syndrome is caused by extra copy of chromosome 21. The risk of having 2nd child with Down syndrome because of this mechanism is quite low (<1%). If translocation in dad is the cause, risk is 3%; if translocation is in mom, risk is 10-15%. See: http://www.Mayoclinic.Com/health/down-syndrome/ds00182/dsection=causes.