I have too Logitech F710 and i have saw this issue with Gran Turismo 2 and lr-pcsx-rearmed. During the race, sometimes, the controls are freezing, for example, i can't brake or turn the car. To fix this i have increase the psx cpu speed from 57 to 67 for this game. I didn't notice it with other emulators because i use the controller only with the games that support vibration.

I have saw the same issue with the same game and controller with other gaming distro and is more noticeable there.

With Logitech F310, that is not wireless, i don't have this issue.

That means pcsx2 didn't install properly. Try re-installing and then look in the last log file under $HOME/RetroPie-Setup/logs to see if there are any errors related to the installation.

@JJRambo the point is that only the creator knows what is in his creation.
This concerns all kind of things, not only a retropie-image.
So i have no idea who you could ask to get a really good answer.
You could ask people somewhere else what they are guessing.....but in usual it does not help.

@Dyelon hey pal, did you ever get it fixed? Having exact same issue as yourself. Bought USB encoders from amazon same thing.

There doesn't seem to be anything special about the devices - I see you only have 1 gamepad (which is considered by mame2000), but there are also a few keyboard and mice attached. Barring any permission problems (unlikely), I don't see why RetroArch excludes them - might be something to do with the core ?
Can you try running with Mame2003 or other RetroArch core (FBAlpha) to see if this changes anything ?

@canispeaktodave Hi, I have an lcl piboy allso and am so happy to learn here that with a dongle in the usbport, the dropped button presses are over! It really makes a huge difference! Thanks for the tip. Did you eventualy come up with a perminent solution or did you stuck with a dongle in the usb port?

It might be worthwhile to uninstall and reinstall the Xpad driver. After my last update, I had to do that inorder to get my 8Bitdo controllers to fully function again.