Microsoft has released new hotfix rollups for both FIM 2010 and FIM 2010 R2. Among other things it is said to fix the “stopped-server” error in FIM 2010 Synchronization Service.
Read more at FIM 2010 hotfix rollup (build 4.0.3627.2) and at FIM 2010 R2 hotfix rollup (build 4.1.2515.0)