There is a company in the UK called HappyDayz Ltd that offer a repair service. Here's a link to their site, and specifically to the 3G MMI High:
https://www.hazzydayz.com/mmi-3g-bas...ate-8536-p.asp
Their prices are listed as 'Supply & Fit', so I'd suggest contacting them to see if you can send them the part for repair, and what the cost would be.
Depending on that, you might want to consider the other option of just buying a new one. Our forum sponsors have them for sale on eBay, or at least I believe so, as the centre control button has the small joystick on top.
https://www.ebay.co.uk/itm/192954474927
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2001 A8 D2 FL 3.7 Q - LPG Conversion, Engine: AKC, Gearbox:FBB, Colour:LY5X Aqua Blue pearl effect, Interior:WJ light beige/dark beige valcona leather with burr walnut inserts
My DIY jobs -
Replaced alarm horn,
Replaced Coolant Temp sensor,
Updated RNS-D firmware,
Installed Reversing Camera and Digital TV,
Dashcam Installation,
Retrofitted Rear Blinds,
Auto-Dimming Rear View Mirror,
Chrome Boot Struts
Sold! 
2008 S8 D3 5.2 V10 - Engine: BSM, Gearbox:KLW, Colour:LY7F Suzuka Grey Pearl Effect, Interior:Black/Black with Silver/Black valcona leather with carbon atlas inserts, Bang & Olufsen, Heated windscreen, Soft-close doors, TV, DAB, AMI, Quad Zone, Auto Boot, Auto dim Mirrors, Keyless entry, PDC with rearview camera, AFS II Headlights
My DIY jobs -
Fan Jet Windscreen Washers,
Retrofitted Electric Side Blinds