In order to replicate, a probe needs material from the star system it's visiting, stuff like iron and silicon. That process is likely to break down after so man

In order to replicate, a probe needs material from the star system it's visiting, stuff like iron and silicon. That process is likely to break down after so many journeys, so no more replicants. The probes would put their own AI into the child probes, including their own random defects. It would take a lot of trial and error, each trial being thousands of years, for the likely success of a single journey's replication to exceed the combined half lives of breakdowns and AI degeneration.