Some portion of the JVM is being swapped out by the operating system (OS).
Check your system.log for messages from the GCInspector. If the GCInspector is indicating that either the ParNew or ConcurrentMarkSweep collectors took longer than 15 seconds, there is a high probability that some portion of the JVM is being swapped out by the OS.
One way this might happen is if the mmap DiskAccessMode is used without JNA support. The address space will be exhausted by mmap, and the OS will decide to swap out some portion of the JVM that isn't in use, but eventually the JVM will try to GC this space. Adding the JNA libraries will solve this (they cannot be shipped with Cassandra due to carrying a GPL license, but are freely available) or the DiskAccessMode can be switched to mmap_index_only, which as the name implies will only mmap the indices, using much less address space.
DataStax recommends that Cassandra nodes disable swap entirely (sudo swapoff --all), since it is better to have the OS OutOfMemory (OOM) killer kill the Java process entirely than it is to have the JVM buried in swap and responding poorly. To make this change permanent, remove all swap file entries from /etc/fstab.
If the GCInspector isn't reporting very long GC times, but is reporting moderate times frequently (ConcurrentMarkSweep taking a few seconds very often) then it is likely that the JVM is experiencing extreme GC pressure and will eventually OOM. See the section below on OOM errors.