The Driver You Need
I thought I'd answer your question, since by asking it, you answered my question. I have the same phone as you and was having the exact same issue. You do indeed need the drivers for the phone and those drivers are indeed actually on the device when you plug it in via USB. And yes, they disappear just as you said. Same thing happens on mine. I actually didn't know they were there at all until you asked why they were disappearing.
The only way I've found to get these drivers is to be REALLY fast when the drive pops up. The only file you actually need is the file called "PTAPC_V1_1_6_0630.msi". You have just under 20 seconds to copy it. I figured this out by coping the "USB_driver_installation_guide_v0.5.pdf" file which told me which files to grab. The file is small, so you have time to copy it.
I hope this helps.