Hello Agostinho,
looking at your network diagram and your show output commands we see the following:
the destination network of your ping test is the R2 loopback address 172.20.10.1
I suppose your ping test is started from R1.
The best path ( = successor in EIGRP terms) is via Fas0.6 from R1.
During the ping test from R1 you shut R2 fas0 interface that leads to R1.
How is R1 connected to R2? I see that on R1 you have two Vlan based subinterfaces one Fas0.6 connecting to R2 and Fas0.7 connecting to R3.
It is clear that you have a LAN switch in the middle interconnecting R1 to R2 and to R3 with all the router Fastethernet ports connected to different switch ports.
So, when R2 fas0 interface is disabled, R1 fas0 and fas0.6 interfaces is still up/up.
EIGRP hello timer is 5 seconds and EIGRP hold time is 15 seconds. R1 detects R2 failure when the EIGRP hold time expires that is within 15 seconds.(after 15 seconds from last received EIGRP hello)
After that, R1 declares down the neighbor with R2 and looks for an alternate route to 172.20.10.1.
The alternate path is via R3 but it cannot be used immediately, because it is not a backup path ( not a feasible successor in EIGRP terms).
So you should see with appropriate debug commands that R1 goes active for the prefix sends out an EIGRP query and receives a reply from R3 and only at that point it installs the alternate route and ping is successful again.
The main reason is the use of the LAN switch in the middle. Then there are some specifics about EIGRP behaviour that I haven't detailed.
EIGRP is very fast when a backup route is ready to be used in the EIGRP topology table ( feasible successor).
From the point of view of R1 it has no feasible successor for the route 172.20.10.1 via R3, because R3 EIGRP metric (advertised distance in EIGRP terms) is greater then the best metric on link R1-R2 (called feasible distance in EIGRP terms) a serial link compared to a Fast ethernet link greater delay and a lower bandwith that increases the metric.
Hope to help
Giuseppe
