One of my favourite verses in the Quran is the following one related to your question.
"And when My servants ask you, [O Muhammad], concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me. So let them respond to Me [by obedience] and believe in Me that they may be [rightly] guided." Holy Quran, Chapter 2; verse 186
God tells us in this verse that he is near to all of us (i.e. accessible to all human beings) and God responds to the prayers (invocation) of the person who sincerly prays to God. So our response to this promise of God to all human beings should be to believe in Him and to make our best effort to follow His guidance.
Another one of my favourite hadiths (sayings) of the Prophet Muhammed Peace Be Upon Him is the following one.
'Fear the prayer of the oppressed person, even if he is a disbeliever, for there is no barrier between it and Allah' [Ahmad].
Now does that mean according to Islam that everyone gets what they pray for? No. If you ask for something and you don't get what you specifically asked for, it doesn't necessarily mean Allah (God) didn't accept your prayer (du'a) or that it didnt work. Our prayers can be accepted (or unaccepted if we pray for evil things) but can be responded to in different ways.
- You can get exactly what you asked for when you asked for it e.g. pray to get a particular job or get accepted in a particular school and you get it.
- Your prayer is accepted but is answered at a later date sometimes with something even better then what you initially wanted e.g. when I was 9/10 I prayed to God to give me a new bike. Though I didnt get it that year, the following year (or later on in the same year - my memory is a bit foggy) my dad bought me a brand new bike with 15 gears that was my favourite colour and lasted me till I was 16/17 years old. None of my brothers or sisters ever got a bike as new or as good as mine (in my opinion ). I didnt get the response to my prayer straightaway but eventually got exactly (or even better) then what I asked for.
- God accepts your prayer but answers it not by giving you what you want but by removing something harmful that was supposed/destined to happen to you in the future e.g. an illness, accident, loss of job, family tragedy etc.
- God accepts your prayer but it is answered in the form of numerous rewards in the hereafter to the extent that you will wish that none of your prayers had been answered during your life (paraphrasing from something I heard a while ago. Cant remember if it was a hadith or not).
With regards to the case of April Jones I cant give you a specific answer because obviously I cant speak for God but will just be quite general.
Sometimes things are destined to happen and so your prayer can not be answered in the way you want. For example if a family member is terminally ill and you pray for them to be healed if it was destined that the person would die at that particular time in that particular way, no matter how much or how many people pray for that person it has to come to pass. But your prayer may be answered in a different way so it still doesnt go in vain.
Also sometimes you may pray for something thinking that it is good for you but it actually might be bad for you so God does not give you that thing you asked for. I think alot of people can think of situations when they really wanted something but didnt get it and later on saw the benefit of not getting that specific thing they asked for. This can also apply the other way round where you can really hate something but actually through going through a particular experience you can actually come out better for it.
"And it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. Allah knows but you do not know". Holy Quran, Chapter 2; verse 216.
For example we all hate getting sick but when we get sick through the process of our bodies fighting off that sickness we gain immunity from that disease. So in the long run that experience of getting sick (which we dislike and can be unpleasant) helped us to become stronger.
I hope this makes sense.