Hey Stich,
Having the same issues, You start the car and its fine for god knows how many K's you drive (did about 20km), but as soon as you stop it and then attempt to start again <2-3mins the HICAS warning light comes on and the system is completely out heavy steering ect. If I leave it for 5mins then start again its fine. I've been able to reproduce it easily but having a aftermarket ECU is making it hard to diagnose.
Pulled the HICAS ECU from the boot replaced the cap that was leaking (C35) also did 2 others next to it while I was at it. I thought I had fixed it but on a quick test run up the road pulled over, switch off then on again and the light is back on and get the same symptoms. Also checked connectors on the HICAS motor @ the rear diff - cleaned with contact cleaner. Again no fix
Its been fine until today where I noticed it for the first time ever. Battery has been swapped out, upgraded the power and earth cables ect(needed a new batt anyway) - this was done before I replaced the caps as above no fix. Prior I put a earthing kit in the engine bay - which is the only large change to the electrics system. Prior to that the dash was out for a heater core but at the time It didn't have issues (a few quick stop and starts while bleeding air ect).
From my limited knowledge of electrics - it definatley seems related to power. Exactly where the issue is has got me. Thinking the rain while driving this morning, but have been driving in rain for the past 3 weeks and never noticed it.
I'll look around the engine bay tommrow, then to the steering position sensor behind the steering wheel. Also hunting a stock ECU for diagnostics.
EDIT: Forgot to mention the car, 94 R33 S1 GTS-T. Only owned it for 6mths but the HICAS system has been serviced - to my knowledge by a Redcliffe company (Brad steering, brake something.)