I saw your thread asking about the internal battery/FRLG effects. I've heard (not 100% sure, but very likely) that when the R/S internal battery dries, the game clock becomes the same as FRLG's. (It takes longer for SRs, though, since it displays the annoying message each time!)
For FRLG, the random numbers don't shuffle like they do on the other games, so you need to resave every 25 SRs or so to reshuffle the numbers. You might find yourself seeing some of the same Pokemon when you SR, since the numbers don't shuffle well.
If you resave every once in a while, though, you should be fine. Lots of people have gotten shinies on FRLG, so you should be fine getting them on R/S post-internal battery death.