shiny-server is eating up hard drive space

I've been running Shiny Server (v1.5.5.872) on Ubuntu (v16.04.3 LTS, AWS EC2 t2.2xlarge) for a few months now, but this issue came up only recently. (It's usually just myself running Shiny apps, with an occasional user or two accessing them as well.)

The available hard drive space is going down pretty fast. This stops as soon as I run

systemctl stop shiny-server

I don't remember this being an issue until very recently, and I'd appreciate any tips as to what may be causing it, and what I could do about it.