Try giving the steering column cowling a bit of a knock from underneath when it does it again. Not too hard- just enough to get it's attention. I see this quite a bit on this generation of Audis (B5, C5 and D2) and its usually the connector to the immobiliser reader coil on the ignition barrel. A bit of percussive maintenance is just enough to make the connection again so the ECU can read the key.
The longer term fix is to dismantle the cowling to get to the connector and then just disconnect & reconnect it a few times, then give it a tiny squirt of WD40.
The contacts are very small in this connector and not very well supported. I think they just become a little loose & dirty with age.
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