I've posted about a similar issue before, but unfortunately something similar has happened. None of the PS1 games on vizzed are allowing me to use the analog sticks on my controller (a PS3 controller). The controller works perfectly fine otherwise, all the buttons respond, the analog sticks work fine everywhere else (include a playstation emulator I downloaded just to test if this was a controller issue or vizzed issue), and the drivers are up-to-date and installed. I can even configure the analog sticks to other buttons on the PS1 emulator here. Anything involving the actual analog sticks and their use for the game just flat-out do not work. I've had them work in the past but I feel like I've tried everything (reinstalling motioninjoy, reconfiguring, everything) and I have had zero success. Does anyone know what could possibly be the problem?

How is your controller connected to the computer?

vanelan : It's a wireless Bluetooth PS3 controller. It connects via a Bluetooth USB adapter that came with the controller. 

Well, I mean what driver do you use?

vanelan : Oh haha, sorry. It's listed as an HID-compliant game controller in the devices and a Motioninjoy Virtual DS3 in Better DS3.

I would recommend  uninstalling motion in joy. 
It causes a lot of problems. 

I would personally recommend SCP DS driver. 

vanelan : I took your advice, painstakingly removed every scrap of motioninjoy (an incredibly frustrating process), and installed SCP DS. My computer recognizes the controller fine, including the analog sticks. Tested it out in PCSX2, it works perfectly. Try a PS1 game on Vizzed...unfortunately, the analog sticks still are not recognized (the other buttons are still working fine). What could be wrong?

They act kinda strange...if you push and hold a direction when remapping the controls, it should recognize them.

Otherwise, you might be stuck using the d-pad.

It might just be because the analogs are recognized as hat switches.

But anyway...try to remap the controls. When it asks for a direction, move the stick in the direction you want it to map to and hold it for a few seconds.
Otherwise, try to move it in the direction twice. (ie: Up, Up) and see if that works.