Could it be that they just feel they are now too old? My parents used to have my brother's children every school holiday... and they were great at first with my kids. But then they just got too old and my mum developed dementia over the years and is now in a home. So whilst they were in a position to look after my brother's children, I couldn't possibly leave my kids with my Dad although he can do short periods of time. He just gets too tired. His situation is different now, than when my brother's children were little.
I would ask your in laws if there is a reason why they don't wish to look after children anymore... but if they are getting older or feel they're not up to it, there isn't much you can do. You don't want anyone to look after your children just because they feel obliged, especially if they don't feel physically up to it anymore. It is tiring. You could ask around to see if anyone can recommend a babysitter.
We have had some excellent teenage babysitters... but you do have to pay for them.
I would ask if there is some reason and as already said take the answer with good grace, but only because it may be something that affects your whole relationship with them. Grandparents aren't obliged to look after the kids or to have any fantastic reason for not wanting to. If they've always been 'yes' people in the past perhaps they think its about time they said no from time to time or maybe they just want to get on with there own lifes.This mission to 'win' sounds a little controlling, you seem to expect that both sets of grandparents should be babysitting...you had them, you look after them, free babysitters are a bonus not a right.
For them to say they don't look after kids "anymore" implies to me that they feel they have been taken forgranted, and perhaps do feel used as free babysitters, as though this is their duty as Grandparents.
Maybe they resent having looked afer your neice and nephew "all the time", and made a decision not to be doormats anymore. Personally, I would rather pay someone to watch my children than have someone in the family mind them under duress, which may affect the relationship in a negative way.
By all means ask whether the kids have made a nuisance out of themselves in the past, but I wouldnt expect them to reverse their decision, it does sound pretty final. You're right in thinking its not fair to have your parents watch them every time, which is why it would be better to get a babysitter you can trust.
They don't have to. Yes, you can find out why and respond with grace, but if you don't want to, you can just let it be and respect their decision not to stay with the children. I think we must honor people's choices no matter who they are. The fact that they may care for other children in the family is totally up to them. It is their life and their choices. Take what you get, and accept what you don't.
