Canadian Insurance Broker here:

All depends on how you have it set up at your home:

As a personal venture you have nothing to worry about as far as your insurance goes.  If you have a personal machine mining at home, it will have ZERO impact on your insurance.  The Computer(s) would just be your personal property like everything else.

There is nothing as far as I am aware of any clauses or stipulations that say you can not leave your computer on 24/7 nor what you can use your computer for.  If by chance the computer caused a fire, it would be just a normal fire claim.  

If you are storing something at some one else's place, it is not your insurance that would cover the loss, but the owner of that home.  They computer is under their care, so therefore they would be responsible if it caused a loss.

The problem comes when it moves from personal to more commercial.  

Will you be running this as a Home Based Business?  How much Annual Income?  

From my experience Mining from home would closest to the Data Processing Service.  Which from the companies I work with is acceptable to all of them.  From my experience most will not insure a Home Based Business if the annual revenue is $150,000CAD or higher.

Under home insurance Your Data is not insured(There is limited coverage to rebuild databases and such...but nothing for the Data itself).  So if you have BTC in a Wallet on that computer and it dies...the BTC could be lost forever.

Also there are limits to equipment that will covered under the Home Based Business Insurance.  $20,000CAD is normal, so a few powerful machines and you are already maxed out.