Why didn’t EVE recognize the little cockroach as a living organism just like the plant? The cockroach possesses all characteristics sustainable in life as the plant with the exception of reproduction, although neither does the plant that has yet to show signs of reproduction.
As you can see from this DVD insert (describing the various robots and their primary focus) EVE is an Extraterrestrial Vegetation Evaluator. Her main focus is to review organic, read plant organic, life on the planets that she surveys.
As such, a life-form other than a plant wouldn't register on her scanners.
WALL-E’s visitor is a probe-bot who has been sent to Earth to check for signs of plant life. The Extra-terrestrial Vegetation Evaluator, otherwise known as EVE, takes her mission very seriously.
You might want to note that on a purely personal level she absolutely does recognise the roach as a living being.
Eve finds the insect intriguing. Lowers her arm. The end separates into individual hovering sections...
But when she scans Wall•E and the cockroach together, she finds that they're simply "not what she was looking for" (e.g. plant life).
She let the roach get closer. The little bug intrigued her, and she let him crawl up her arm. WALL · E heard her emit a series of electronic beeps. She was giggling! The roach must have tickled her.
She slowly approached the shivering box. The cockroach ran down EVE’s blaster arm and hopped onto his master. EVE’s blue light scanned WALL·E. NEGATIVE. He was not what she was looking for. She retracted her blaster arm and glided away.
Unlike a plant, a cockroach does not show that the planet has started to recover, just that it has not yet run out of food waste yet.
More importantly: "EVE" stands for "Extraterrestrial Vegetation Evaluator" - as the name suggests, she is specifically designed to search for Flora, not Fauna, (i.e. to search for Plant Life, not Animal Life).