Since Platform as a Service is a no go, what about Infrastructure as a Service (IaaS)? IaaS provides a raw virtual machine that can be configured as needed. Examples of this are Amazon EC2 or Microsoft Azure Infrastructure Services.
Since you have full control, the random restarts are no longer a concern. However, since you have a raw VM, all of the support is left to the developer or operations team. This works well if you have a good system administration team behind you.