Just tried mine and it is working fine (iPhone X, iOS 12.1.3)
Is your DND while driving setting in the Settings set to manual - perhaps one of the automatic or bluetooth options are turning it off? This doesn’t seem to make a difference on my phone, but something to rule out.
What happens if you tap the DND moon in Control Center? Does DND stay on then or does that turn straight off, the same as the driving option?