Question : Is there always a feasible successor in EIGRP ?
Background: An operational route is passive. If the path is lost, the router examines the topology table to ﬁnd an FS. If there is an FS, it is placed in the routing table; otherwise, the router queries its neighbors, sending the route into active mode.
Answer: There has to be an more than one path between two routers for a feasible successor route to exist. If there is only one route, then there can be only one successor and, of course, there must not be a “feasible successor” route for the alternate path because there is only one path.
Note: As Gary notes in the comments below, a route must pass several pre-conditions. In order to be considered a feasible successor, the Reported Distance (RD) of another route must be lower than the Successor route’s Feasible Distance (FD). RD is what your neighbor is reporting as their cost to reach a specific network. The FD is your cost to that neighbor, in addition to that neighbor’s RD..