Why unidirectional ping in LAN?

My LAN looks something like this, with R1 = normal router and R2 = wireless router :
 
Internet ----- R ----- Desktop
               1 --+
                   |
Nothing ------ R --+
               2 ----- Laptop
 
The problem I'm trying to figure out, is why the laptop can ping the desktop but not vice-versa.
 
I'm imagining the ping from the laptop hits R2 who notices the destination address is inside the subnet, so he repeats that packet on all his LAN ports, one of which is R1.  R1 sees the ping, notices the destination address is inside the subnet, so he repeats the packet on all his LAN ports, one of which is the desktop.
 
So why doesn't it work the other direction?  Is the fact that the laptop is connecting wirelessly relevant somehow?
 
Thanks!
Chris