Mactoyz, in an unhelpful way you are turning a deliberately blinded eye to most people's clear, observable findings and ridiculing the real-life solution experienced and offered here to others, many times.
Like others, I have reset the PRAM and other 'fixes' as suggested. These processes made absolutely no difference to the lack of connection: absolutely NO difference.
Like many others, I have checked the fit of the batteries in the housing and I can plainly see that this is one poor design of battery housing. To remedy it, I have adjusted the fit of the batteries to ensure that they
1) make contact,
2) maintain contact.
Standing on one leg or spinning a ball is not involved in any way. Why you infer that, I have no idea.
What IS usually required is to remove the wrapping & insulation (unfortunately) from the +ve end of the battery so that the terminals can actually make proper physical contact. After that, the mouse works. Simple. Fact. This is the case with every 'Magic Mouse' that I have for every iMAc at work and at home. Simple fact. The fix has been repeated many times, the latest being last week with a colleague's iMac.
There may be other problems that others including you are having, separate to this,and in that case it's great to have the solution to those problems also, but as this lack of connection is a massive, widespread problem for users, please do not deflect people from a real, straightforward solution that will fix most cases - and please do not let Apple off the hook on this mouse design.