21 months without sleeping

We, the parents of a 21 months old baby, have been during that time without sleeping. My 21 months daughter, awakes during the night, all the nights since she was born. Every night awakes between 1 and 5 times (I have some insomnia problems, and when my daughter wakes me up I cannot fall asleep again; many nights I sleep 2 or 3 hours max).

Since a couple of months ago, she was kept silent and calmed with a feeding-bottle of milk that we usually gave her. We decided to give it to her before we go to sleep, but she still keeps on waking up. Normally she calms down with water. We have tried not to attend her immediately, because what she actually makes is groaning being half asleep, rather than crying, but if we do not attend her, she eventually wakes up completely and begins to cry despairingly.

I've tried with NATRUM MURIATICUM 9CH, 3 little balls once she's already sleeping during 8 days, to check whether it was a thirst problem, but without any result. Now, I'm trying with PASSIFLORA COMPOSE, 3 little balls once she's already sleeping for 3 days. She does not wake up so often, but still does.

My daughter weights about 12 kilograms. She eats very little, but is quite healthy. She doesn't like to try new foods in her meals. She sleeps about 11 hours during the night, and a snooze of about 1:30 hours in the afternoon. She doesn't look sleepy during the day. She sleeps alone in her cradle and bedroom since the very first day she was born. She falls asleep by her own and without crying. During the day she drinks very little water or fruit juices. She hasn't been ill almost ever (just an earache and a gastroenteritis). Lately, she's not very sociable. She is absolutely not sensitive to cold, thus I don't shelter her too much during the night (she moves a lot into the cradle, that's why I don't cover her with a blanket, but I put her to sleep wearing double pyjamas instead). She's a beautiful blonde baby with clear gray eyes and clear skin. She has very marked rings under the eyes, but I believe that's maternal heredity :-D. She also has a very big head (paternal heredity), and a nice rounded face. In some senses, she's a bit behind for her age (she does not speak absolutely anything, even 'dad' or 'mum', though she can say these words and she does, but never to call or refer to us, so it seems to me that she doesn't know what she's saying; and, for instance, she began to walk when she was 17 months), but in some other aspects she goes quite advanced (she perfectly identifies the numerical digits when you ask her where one is among the others, and so she does with lettering, colors, animals, etceteras, and since a long time ago besides).

I believe that, if it were a cold/hot/thrist problem, some night, she should have slept well, although it had been only one, but this has not been the case. I suspect that it's a problem of her habits or her biological clock, but I cannot figure out how to break it.

Thank you for your help.