How do I sync instance A to instance B without losing any of the data already on instance B?
Golden Gate is answer to these types of problem. Oracle bought it. Therefore it is a Oracle Golden Gate right now. 

Look below image which is taken from Oracle Golden Gate Admin Guide
 http://download.oracle.com/docs/cd/E18101_01/doc.1111/e17341.pdf

Also you can look to following article: 

http://www.dbasupport.com/oracle/ora11g/Oracle-Replication-Streams-vs-GoldenGate.shtml



Thanks Tevo D for pointing out licensing issue. Actually golden gate may be a expensive solution depending on your circumstances, i.e your company's standing with Oracle, what is your cost of downtime etc.