4 year old - extremes of energy?

[Djini]

I'm really worried about my DD, who has just turned 4.

(Possibly relevant background: she's bright, independent and tracking on or ahead of most developmental markers except socialisation/eye contact, which the nursery picked up as a potential issue at 2.5. Since then, she's been being monitored by the early help and children's pediatric services, who seem to think she's basically ok, though there may be some indication of high-functioning ASD/aspergers; we're on a waiting list to be assessed for that in due course)

She has two modes: full of energy, running, jumping, climbing everywhere, on everything, plus chatting at a million miles a minutes, engaging with everything and telling stories OR beyond exhausted, unable to function or listen or control her body, can barely stand up or engage brain, acts like she's on a different planet.

She sleeps 7.30ish (bedtime at 7) to 6.30ish, like a log, mostly, with the usual faffing around at bedtime. She doesn't nap at preschool any more, and occasionally at the weekends will consent to nap (only in bed, with PJs on) at the weekends, if we've done something particularly energetic in the morning like swimming or whatever. She won't/can't nap in car, on sofa etc. Can't stop herself fiddling or rolling around if there are distractions or anything stimulating (including her baby sister, or me/DH) around.

Mornings tend to be good from waking up time until about 9.30 - if we're not doing anything by then (going out for a walk or playing somewhere) she starts to "lose it" and become unmanageable: distant and limbs akimbo. She picks up again after lunch (if not napping) and then by the end of the afternoon, 4.30 onwards, she's all over the shop, especially if no nap earlier. I then pour her into bed and the cycle repeats.

Is it normal for a 4 year old to have such extremes of energy? Do you have experience of a 4 year old being so totally exhausted and not switched on? I've tried making sure she has regular (good) snacks, in case it's blood sugar related, but that doesn't seem to make a difference. The only thing that helps is sleep (like a reset button, it's miraculous) but I'm worried that when she goes to school in 6 months or so, napping won't be an option and she'll just end up being non-listening, non-compliant, and non-sensical.

Any thoughts? Thanks in advance.

[Djini]

I should also say: she's not prone to meltdowns or other outbursts, and never has been. But she is quite sensitive and teary, especially when overtired.

[djini]

Hopeful bump...anyone ?