I am researching a similar issue with the c2wts service  not starting and stopping unexpectedly. I found a thread saying there is a know issue withe it starting because a dependency on the crypto service. They recommend adding the dependency manually from SCM or from an administrative command prompt with ?sc.exe config c2wts depend= cryptsvc?.

Sorry, I should have read your link first.Looks like similar information.

in my case it wsa caused because the service  needs access to the Internet
to valdiate a certificate. It will not run through a proxy. For more details
check:
social.technet.microsoft.com/.../6b865ead-970b-4460-9dcf-1cc6d6d8530b