We consider a dynamic fault diagnosis problem: There are n
processors, to be tested in a series of rounds. In every
testing round we use a directed matching to have some
processors report on the status (good or faulty) of other
processors. Also in each round up to t processors may
break down, and we may direct that up to t processors are
repaired. We show that it is possible to limit the number
of faulty processors to O(t log t), even if the system is
run indefinitely. We present an adversary which shows that
this bound is optimal.