So, I realize that this thread is incredibly old, but I just wanted to write in to say that I also had this same issue with certain games not responding to controller input and was able to fix it. I’m using RetroArch 1.2 with Mednafen PSX V0.9.38.6. Basically, by default, I have the controllers set as Dual Shock controllers. This is great for most games, but the issue is that there are certain games (Hot Shots Golf, Fantastic Four, Fox Sports Golf '99, etc…) that will simply not recognize inputs from these controllers. For those games, the controllers need to be set to PS1 Joypads. It’s interesting, I actually ran into this issue while setting up config files to turn on multitap functionality for specific games. I found that there are certain games where the multitap actually works incorrectly if you are not using PS1 Joypads. Frogger, for example, will not recognize player 3 or 4 no matter which port you have the multitap plugged into unless all the controllers are PS1 Joypads and not Dual Shock controllers. Please keep in mind though, there are also certain games that can only be played with a Dual Shock controller (Ape Escape, for example). So, per game configurations may end up being necessary depending on which games you are playing/have.
I hope this information is helpful! Happy Emulating!