Shiny server slows down and CPU spiking after 24 hours of service running

We have Shiny server installed on a centos Linux VM and it runs fine initially after the Shiny service starts up. The webpage loads almost instantly but after the service has been online for 24 hours (and therefore the webpages have been accessed hundreds of times) the pages slow down to the point where they timeout sometimes and CPU on the server is spiking to 99% when previously it was around the 20% mark. There is plenty of free RAM available on the server.

Any ideas please?