Your Wave's battery will continue to drain—very slowly—even when it's turned off, much like any rechargeable device. This is because there are electronics that use a small amount of energy (to monitor temperature data, wait for button presses, measure current battery charge level, for example) even when your device is not actively warming, cooling, or communicating. For this reason, the battery will eventually lose charge over time, even if you're not using it.
On a full charge without any use, your Wave 1 should last about 2-3 weeks before it's completely out of battery. So, if you don't use it for a week or two, you should still have some charge left. If you've pulled it out of a drawer after a month, though, it's likely that you will need to plug it in for 1-2 hours before you'll be able to use it.
If you're seeing that your device is running out of battery much more quickly than this, please let us know!