Firstly, ensure you have the most recent version of iTunes installed on your machine, then:
- Plug in your device.
- Type Windows Key + R, then type
devmgmt.msc in the box which appears, hit enter.
- Click Portable Devices.
- Right click on Apple iPad/iPhone/iPod, then Update Driver Software.
- Choose "Browse my computer for driver software"
- Navigate to "C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers"
This should install the baseline iTunes framework required for remembering your computer's unique address. You may need to trust the computer once more after having updated the Apple iPhone driver software.
Note: You may need to search in some other tabs in Device Manager to find the Apple device, such as Unknown Devices. You'll know when you've found it.