There may be cases where a live migration causes the memory contents to be re-transferred over and over again. This process causes the guest to be in a state where it is constantly writing to memory and therefore will slow down migration. If this should occur, and the guest is writing more than several tens of MBs per second, then live migration may fail to finish (converge). This issue is not scheduled to be resolved at the moment for Red Hat Enterprise Linux 6, and is scheduled to be fixed in Red Hat Enterprise Linux 7.
The current live-migration implementation has a default migration time configured to 30ms. This value determines the guest pause time at the end of the migration in order to transfer the leftovers. Higher values increase the odds that live migration will converge