Chat users are available but a chat remains stuck in the queue

One explanation for this is when agents decline a chat, and there are no more agents the chat can be rerouted to. For example:
 

1. The button configuration has 'Reroute Declined Requests' enabled. 
2. Agent 1 and Agent 2 have the same skills.
3. Agent 1 chat capacity is 2
4. Agent 2 chat capacity is 4
5. Agent 1 is at its max capacity of 2
6. A new chat comes in and is routed to Agent 2
7. Agent 2 declines the chat
8. Because Agent 1 is at capacity, the chat cannot be rerouted and is sent to the queue

When viewing this from the Chat Supervisor tab, you will see that Agent 2 is available and is not at capacity, yet the chat remains on the queue. This is because the chat is waiting for another agent to become available before it can be rerouted. If eventually the chat disappears from the queue and is not routed to any agent, it is possible that the visitor closed the chat window. 

It should also be verified that all agents online that are expected to have chats routed to them have the "Chat User" checkbox enabled on their User record.

How to Confirm This Behaviour?

In order to confirm this theory, or understand why the chat was never routed to an agent, you need to locate the transcript created for that chat (transcripts are created even if the conversation never started; they are created when the chat session ends).

You can find the related transcript by searching for transcripts created around the date/time the chat disappeared. The transcript's body will be blank since there was no interaction and you can review the Transcript Events related list, to understand why the chat was never routed to an agent. 

For example, the Transcript Events will likely show something like this:
 

1. Visitor requested chat.
2. Chat request routed to agent 1.
3. Chat request declined by agent 1.
4. Chat request queued at position 0  (this is when the chat goes to the queue even though agent 1 is available and has the necessary skills).
5. Visitor left.