What happens when an EIGRP router loses its successor and has no feasible successor?

Step by step

1. The successor's link goes down, or it reports infinity. No feasible successor exists.
2. The router marks the prefix A (active) in the topology table and sends queries.
3. Each neighbor decides:
   • It does not know the prefix: replies "unreachable" at once and does not query anyone.
   • Its own successor is someone else: replies with its current distance at once.
   • Its successor was the querying router: it checks for a feasible successor; if it has one it replies with that distance, otherwise it goes active too and queries its own neighbors.
4. The original router waits for all replies, chooses the lowest, and goes passive (P).

What it looks like while it is happening

R1# show ip eigrp topology active

Active routes show A, and neighbors that still owe a reply are listed under "Remaining replies" with an r.

Why it can hurt

The query spreads until it reaches routers that can answer without asking anyone. In a large flat network with no summarization and no stubs, one flapping subnet makes hundreds of routers work, and one slow router anywhere in the chain holds up the answer. That is the setup for stuck in active.