Running router as virtual machine, can it be realible?

There is no reason this won't work, although it's not the way most would choose to do it. One suggestion I would make is to use bare metal virtualization, such as ESXi or Xen Server, rather than using application mode virtualization. Obviously you need to consider the consequences of not having the router available when the host is booting. e.g. You won't be able to manage the machine if it relies on the router being up and for some reason it isn't.

I don't know why this shouldn't be stable and reliable. Depending on the virtualization technique and the hardware, the virtualization of the network might be more expensive then doing it natively.

I ran my router as virtual host on VMWare ESXi. I had no problem doing so and the box was rather reliable as a custom built server. It requires some knowledge on how everything routes together, and unfortunately, I don't really remember how I did everything. The only problem I'm immediately aware of is that VoIP has some issues running as a virtual machine. So you'll need to do some research to ensure that your application will run alright with whatever kernels are available on your hypervisor.

I have been running a VM as a router for a network I manage for over a year through Hyper-V on server 2008 R2. The only things to keep in mind are to disable the host machine's access to at least one NIC you're routing across, and that you'll need to set the VM up to automatically turn on. The setup I have is that the VM routes external traffic into the DMZ and the physical box does the routing for the internal network (3 NICs needed).