I had a similar problem, and found this post by Googling "ip local policy route-map" ssh after several other attempts to find any information about this.
Like the OP, I have an ISR in front of firewalls, and want to SSH from inside, and be able to reach it from my remote office on one of its outside interfaces. I have two inside and two outside interfaces (on separate ISPs), with NAT and PBR configured on all of them, with no default gateway. I could SSH to it from the inside, but not from the outside. The source IP from the inside is on a directly connected network (due to NAT on the firewall behind the ISR), so the ISR doesn't have to route to respond. So, I tried adding an ip local policy route-map, referencing the route map that would send traffic along the desired outside interface. At this point, I lost SSH access from the inside and outside!
From the outside, it was clearly using the route map for internally generated traffic. I could ping it, and it now answered on the outside. If I tried SSH from the outside from an IP address not on the access list, I got "connection refused" right away, meaning the ISR was sending (and routing) the RST. But if I tried from an IP address on the access list, it timed out.
Anyway, by setting a default gateway to route outside, SSH now works both ways (yes, I had to drive over there with my console cable). I also removed the ip local policy route-map, since it's not necessary once a default gateway has been set.
So, somehow if you have NAT and/or PBR configured, the SSH service doesn't work with route maps.
