Definitely agree re bulk inserting, say every 1 minute or 1 hour or whatever.
I was paying around recently with Amazon's Kinesis for this, but if you don't want the vendor lock-in you could easily roll your own system that bundles up events and stores a bunch at once.
You can also bulk insert records, rather than 1 at a time.
We have 2k operations per second on our aws rds.