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It's long been known that the early Exige S cars (Early S cars made in 06) have a possible engine cutout due to a faulty A/C relay module.
The suspected cause of the issue is arching across the relay module contacts which momentarily resets the ECU causing a brief hesitation when at speed.
Lotus issued a TSB (see attached) regarding this issue, and your dealer should be able to remedy the situation under warranty.
If you're like me, my dealer is a 2-hour drive away, so I just ordered the part as I was tired of dealing with the sporadic issue.
The module at issue is the Radiator Fan/AC Module on the attached diagram
Please note that the diagram and description are misleading. The module is "in fact" located on the passenger side wheelarch lining. (When the manual was written, driver's side was intended for right-hand drive cars). I learned this after removing both driver's wheelarch liners, and then eventually moving to the front passenger side wheel liner... Doh!
1. Obtain part number A117M0038F (same part as 05 Elise)
2. Loosen wheel bolts and jack car at front lift point.
3. Support car with secondary jack for safety.
4. Remove wheel
5. Remove wheelarch lining (two bolts in rear, one up top, and three up front). The wheel arch lining is attached to the relay and will not be able to be completely removed until the wiring harness is disconnected.
6. With the wheelarch lining pulled out, you will find the relay attached with two connectors. Use a small flathead screwdriver, to release the "catch" on the harness connections and pull off the module. You can now fully release the wheelarch lining.
7. Using a small flat blade to release the catch on the Relay module that is clipped to the bracket that is riveted to the liner. A feeler gauge works great for this.
8. Clip the new module back on, and reverse the procedure to install.