Brief Answer:
Several possible causes

Detailed Answer:
I read your question carefully and I understand your concern.

First of all regarding toe walking in itself let me reassure you that it is a common phenomenon and in most cases no cause is found and improves over time.

Regarding the Babinski sign, it is true what your pediatrician said that it usually disappears by the age of 2. There may be exceptions but are rare, usually there is another cause. Babinski sign is not really specific, it can be associated with any type of brain involvement. Our basic motor functioning is directed by the brain and spine through a pathway containing two main neurons (nerve cells). The first or upper neuron is situated in the brain and its long projections take its signal to the second or lower neuron which is situated in the spine. So any type of damage to first neurons in the brain or their projections traveling to the spine can result in a Babinski sign.

Now what is the most likely type of damage in a child. The first cause is cerebral palsy, damage to an area of the brain usually due to suffering from lack of blood supply during birth. Brain imaging by MRI should be necessary to evidence that, but even if that turns out to be the case, since you describe no motor deficit or other issue it should be a damage to a small area or would be more visible deficits. So shouldn't worry as it is a process which is finished now, won't evolve and a child's brain should compensate well for it without any consequences.
One other possibility might be a trauma which may have caused a small damage which might have been missed. Again, shouldn't be sizable if gone unnoticed, would be a remnant, sort of like a scar, won't evolve and should hinder your child's development.
Another cause would be a remnant of a meningoencephalitis, but you do not mention any such diagnosis in previous years.
Other causes may include muscular distrophy, tumors etc, but usually would be other prominent symptoms and signs noted by the pediatrician, so unlikely.

So brain imaging might be necessary to determine the cause, but in the meanwhile if the child is completely healthy otherwise, should stay calm as it shouldn't be a threatening issue.

I remain at your disposal for other questions.

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Brief Answer:
Read below

Detailed Answer:
Usually for active lesions there would be other signs, most notable motor deficit (weakness) visible when walking. For tumor also headache, vomiting, for infections fever, headache, vomiting, mental status alteration and so on.
As for MS at that age is not a likely diagnosis. So since you do not describe any symptoms and the child has already been examined by a pediatrician I would say it is unlikely. It can not be completely excluded as with children communication and examination has its difficulties and subtle symptoms may escape, but unlikely.

Regarding absent Achilles reflexes I wouldn't say it adds much, as it doesn't indicate any brain damage, actually in brain lesions Achilles reflex is increased, so it simply may have been difficult for the examiner to elicit the reflex (it may require more experience and technique in children, the neurologist may elicit it).

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