To avoid this you have two choices:
1. delete snapshot (VMware recommends preserve a snapshot for only 24-72 hours)
2. move the VM to a datastore with sufficient space to support the growth of snapshot
When you create a snapshot from a VM, a delta disk is created and over the time this disk can have to the same size as the original base disk, and this explain why you running out of space and datastore and why the VM stop to respond.
Check this KB article for some best practices about snapshots: Best practices for virtual machine snapshots in the VMware environment (1025279)