PlayStation Classics Unplayable On Older PlayStation Consoles

It looks like some of the classic consoles have run into a problem, and it creates an even bigger issue for the future of these said consoles.
As stated by multiple reports, consoles like PS3 and PS Vita have trouble booting some digital games, such as the PSOne Classic version of Chrono Cross, where the console shows a pop-up informing its user of an expiration date and refuses to boot after. You might say that this is because this particular game has gotten a modern version, but older games have been doing this too.
Final Fantasy VI, Run Factory: Oceans and Unit 13 are among the games that are currently unplayable and classified as “older games”. This problem comes after Sony decided to cut PS Store Support for PS3, Vita and PSP, but later decided not to do that because many players negatively reacted to this news.
Sony is yet to comment on this problem.
Have you run into this type of problem? Is there any solution to it?