To get some ideas on what's happening to your VM, you can use the
Google Cloud Console, go to Compute Engine -> VM instances, click on name of the affected VM and take a look to the output of Serial port 1 (console). If you can find some activities or errors that correlate to spikes of your VM's CPU that would be good point to start investigating the issue.
Interacting with the Serial Console is another method that can help you to get into the VM while SSH is not working to inspect and troubleshoot malfunctioning instances. If you've customized your VM by installing some softwares or services make sure that the VPC firewall rules locked down to only allow ingress from and egress to authorized hosts.
I hope this helps.