The battery in the watch is failing to hold its' charge.
It needs to be replaced. Even rechargeable batteries have a life span.
Here is the Ifixit guide on how to replace the battery in your watch.
Motorola Moto 360 Battery Replacement
Here is a link to just one supplier of the battery. It is not a recommendation to use them, it is shown to give an idea of the price. There are other suppliers online that may suit you better, just search for Motorola Moto 360 battery to get results.
Hopefully this is of some help.