Hmmm, that's an interesting problem. Normally when a vehicle dies without a CEL the problem is something physical/mechanical (not a sensor or parts controlled by the ECU) that has failed, the first things I'd check are fuel delivery and spark.
Normally when a fuel pump goes bad they fail suddenly and completely; since the car runs better at speed I'd say the fuel pump is probably not the culprit. That still leaves other items in the fuel delivery system: filters, fuel pump relay (multi-function relay unit), immobilizer, inertia switch, fuses (R1, 20 amp; R2, 3 amp), and the wiring that connects them.
Ignition issues could cause the problems you describe, but the failure mode makes it a little less likely as weak or failed ignition coil (or wiring) could cause this and not trip a CEL.
Another area that can potentially be a cause would be the Idle Air Control (IAC) valve. If these get dirty they can become sticky and not move freely to where the ECU has directed, this can cause rough or unstable idle speeds. Many times a bit of carburetor cleaner can clean them up easily.
I'll attach a copy of the colorized wiring diagram I made for the 2005 Elise in case you need it for your troubleshooting. Good luck and let us know what you find.
2005 Ardent Red Elise, Gut Sport wing & splitter, custom diffuser, Sector111: DSBrace, gPan3, subStuffy2, Larini Sport muffler, decat pipe, Schroth Racing 5 pts, wheel studs, Team Dynamics 1.2 with Hoosier A6s, Koldflash 200 ECU flash, BOE rear clam hinge, BC Racing single adjustables, Hawk pads, SS Brake Lines, HID lights, custom tail and high mount brake light...and much more...