I've seen several status updates on Bluemix saying that applications are being restarted and there will be issues logging in, e.g.
During this time, you might experience temporary errors logging into Bluemix or managing applications, such as starting, staging, and so on. If this situation occurs, retry the operation later. The latest status will be available at http://ibm.biz/bluemixstatus throughout the upgrade process.
Existing applications will see a brief restart of instances, but near continuous availability is expected.
Is it possible then to build a high-availability application on Bluemix?
IBM Bluemix supports deploying applications in multiple different regions.
Minimising downtime during platform issues can be achieved by hosting your application in multiple regions simultaneously and using an external load-balancer to move traffic between the instances depending on availability.
Replicating application data between regions will be dependent on the individual services you're using. For example, Cloudant supports multi-master replication, allowing you to failover without any manual intervention.