Slow shutdowns sometimes on RDS Postgres

Hi,

I'm using AWS RDS Postgres (9.6.6) and have run into very slow shutdowns
(10+ minutes) a few times when making database modifications (e.g. reboot,
changing instance size, etc.). Other times, it shuts down quickly (1
minute or so). I have not been able to figure out why sometimes it takes a
long time to shutdown.

When it happens, I see a bunch of lines in the postgres log like the
following over and over (almost every second or two) during this 10 minute
shutdown period:
2018-09-12 06:37:01 UTC:XXX.XXX.XXX.XXX(19712):my_user(at)my_db
:[16495]:FATAL:
2018-09-12 06:37:01 UTC:localhost(31368):rdsadmin(at)rdsadmin:[16488]:FATAL:
the database system is shutting down

Once I start seeing these messages, I start manually shutting down all of
our applications that are connected to the db. I'm not sure if shutting
down the apps fixes it or if there's some timeout on the RDS side, but it
seems like once I start doing this, the database finally shuts down.

When it takes this long to shut down, it ends up causing a lot more
downtime than I would like. I've tried asking AWS's support why it takes
so long to shutdown sometimes, but they basically just told me that's "how
it works" and that I should try to shut down all of my connections ahead of
time before making database modifications.

We just have a few ruby on rails applications connected to the database,
and don't really have any long running or heavy queries and the db is under
very light load, so I don't understand why it takes so long to shutdown.
We do have a sizeable number of connections though (about 600) and there
are two replicas connected to it. I also tried
setting idle_in_transaction_session_timeout to 300 seconds to see if that
would help, but it made no difference.

I was wondering if anyone else had seen this behavior on their RDS Postgres
instances or had any suggestions on how I could shorten the shutdown time?

Thanks,
Chris