Maybe try Fusion Reactor or something similar?
If you have CF Enterprise sometimes CF Monitor can be assistance to notice what is happening.
It is fair to say on 64 bit the initial and maximum memory setting plus MaxMetaspace of 256m, 512m and 192m respectively can be small. While some kind of Java logging or monitoring can assist to check how well those are performing perhaps you can be better served to increase one or more of those values.
We have CF Enterprise and I have enabled alerts with CF Monitor for memory, slow response etc. But nothing was triggered prior to our external website monitor detect the website has stopped responding.
We have increased the Java Heap Size to 4086MB. Is the Metaspace different to this?
Yes Metaspace is different being non heap. If you have available memory perhaps adjust it EG:
CF Monitor memory only shows you heap usage. So if non heap memory was having an issue it will not be noticed. There are other non heap memory spaces than Metaspace like Code Cache and Compressed Classes (this one enabled Windows Java 8 64 bit I am not sure on Unix) however those filling therefore causing a crash are less likely but should not be overlooked.
HTH again, Carl.