As for platinum and rhodium, palladium discovery comes quite late in human history. William Wollaston (the same man who identified rhodium [link]) was discovered and named in 1802. After a brief moment of skepticism where the metal was mistaken to an alloy, it follows a long period where resources were limited in the extreme.
As for the platinum, large resources of palladium were found in South Africa; and unlike platinum, there were discovered large quantities also elsewhere, in Russia. The metal is therefore somewhat better distributed than platinum, but barely. The two countries share almost perfectly 80% of the palladium supply; the remaining small producers include the USA, Canada and Zimbabwe.
A major problem for palladium is that the potential reserves are poorly estimated. Not knowing what would remain in the soil, it is difficult to estimate how long you can still use the existing veins. In addition to this problem is the fact that the Russian government wants to limits its export of palladium . Fortunately, a huge potential deposit is being studied in the Philippines.
If we are immune from a palladium shortage for now, we will have to seriously evaluate the resources available in the near future!