The case, which began in earnest in February, was not expected to continue beyond early April but the examination of witnesses is taking much longer than planned.
Already the hearing has cost millions of pounds, and has beaten the 30-day record for a High Court IT battle.
Unless there is an early settlement, the case is due to continue into May and could run into June. The legal costs could exceed £5m, a bill that the losing side could be ordered to pay.
If Nats loses, it also faces paying more than £42m in damages to EDS which, with interest, could bring the final bill to nearly £50m. This would eliminate the advantage of the £30m emergency loan from the Government to help Nats meet its financial commitments.
Instead of a forecast profit, Nats is facing an annual loss, because of a fall in income from airlines after the events of 11 September. It is facing further financial pressure because the Civil Aviation Authority is expected to reject a Nats request for a 5% rise in charges to airlines for air traffic control services.
The High Court hearing arose when EDS sued for more than £42m after Nats terminated its 14-year private finance initiative contract in July 2000, 11 years early without sufficient reason, EDS claims. Nats is counter-claiming £8m and says it ended the partnership because of EDS' failure to meet a critical milestone.
A spokesman for the airlines that own 46% of Nats denied that the High Court case was adding to financial pressures. He said the sums involved were not large in relation to Nats' business.