AWS RDS: How do I diagnose this failure?
I have had this happen, even to production RDSs, though it is rare. 

How to go about diagnosing

Check there was no advance notice of maintenance work:
Did you get any email notifications from AWS to say that your instance needed mandatory system upgrades or maintenance?  Was this in your instance's permitted maintenance window?

Raise a ticket with AWS Support:
If you have AWS support, raise a ticket with them to ask them what happened.  On the occasions that this has happened and I have raised a ticket they were not able to give me a good reason for the DB going away, but have generally shrugged and named local networking issues on the instance's HyperV.

Did I loose data?
It's unlikely though that you lost data if you are using innoDb and it was a shutdown issued by AWS. The log lines that you cite:
"Giving 2 client threads a chance to die gracefully", then 
"Shutting down slave threads"
Are lines from a command initiated shutdown, rather than a crash.  It looks like AWS issued a shutdown for you.

Other Notes
Occasionally AWS sees fit to move your instance to another Hypervisor without prior notice, sometimes because they want to clear the Hypervisor that your instance is on, it may have developed hardware problems, for example.
There might be networking issues within AWS, or you might be subject to 'noisy neighbours'.  There are many possible reasons and unfortunately contractually AWS don't have to tell you why.