The Little Green Button can go grey for a couple of reasons.
The most straight forward one is a situation where the button is 'alone'. There are no other buttons available to receive an alert, and therefor the button will turn grey to indicate there is no help available. This can also happen when a button is isolated inside a separate subnet to other buttons and your licence is set to the Island option of the Connectivity models.
When there are multiple buttons, but they are all set to the same location, they will all be grey. This is by design on the premise that when a situation arises in a specific location, everyone in that location will be aware of the situation. Additionally, it will allow for a 'silent alarm', when an alert is sent out, PC's around the orginating alert won't give off an audible signal.
There is a few scenarios where the button could be thinking it is 'alone', when it is not.
The most common underlying cause for a grey button is the service is not running. To ascertain if this is the cause, please follow the steps outlined in this support article.
Another cause could be that the button is unable to see other buttons because of network restrictions. There are a few prerequisites that need to be in place for the Little Green Button to function as intended. These network requirements are outlined in this support article.
If there is a calendar icon showing inside the grey button, that means the licence is expired. Please see here for steps to be taken.
If there is a key icon showing inside the grey button, please follow this guide to get the button activated.