VS not pass traffic to pool member

Change your route on the server (10.0.2.101) for 10.0.1.244/32. The next-hop should be the BIG-IPs self-IP (floating, if available) in vlan 10.0.2.x, not the VIP for the VS.

I'm making some assumptions based on lack of info, but I assume your BIG-IP and server (10.0.2.x) are on the same network.

The route that you have specified (10.0.1.244 255.255.255.255 10.0.1.204) has a next-hop that is not on a directly-connected network of the server. This won't work unless the server can recursively find a route that provides a next-hop on a connected network. I'm assuming your BIG-IP has a self-IP in the 10.0.2.x network, as when you enable auto-map the BIG-IP will (preferentially) SNAT traffic to the floating IP on its egress VLAN.