Definition - What does Flapping Router mean?
A flapping router exhibits the condition of transmitting routing update information about a network destination via one route and then another in a rapid sequence. Route flapping happens when there are pathological conditions such as hardware, software or configuration errors found in the network that causes certain information to be repeatedly advertised and withdrawn.
Techopedia explains Flapping Router
In a network where a link-state routing protocol is run, the flapping router will force all connected routers to frequently recalculate topology. In networks that use distance vector routing protocol, flapping routers trigger routing updates whenever there is a change of state, so in both cases the constant route flapping prevents the network from converging.
Route flapping can be minimized or contained within a smaller portion of the network when route aggregation is used. An aggregate route will not be released when there is still at least one valid aggregated sub network. This occurs because a flapping route that is part of the aggregated subnet will not affect the routers that receive the aggregate.