Hey Taith,
Based on what you are describing this sounds like your World connection is getting dropped, while your Home connection remains connected. Home is responsible for your chat, while World is responsible character movements, abilities, looting, etc. We created a post on the difference between the two here
Your World connection will send a lot more data than the Home connection, so World is more susceptible to things that can cause interruptions or disconnections. Wireless connections, packet loss, router issues, and issues between your internet provider and the WoW servers are all common causes for this.
One thing to keep in mind is that each game / application is different in how it handles the connection. Some may be more resistant to brief “hiccups” in the network connection, while others can be more sensitive to them. So it is definitely possible to see issues with just one application like WoW and not have issues anywhere else.
Are you using a wireless connection, and if so are you able to switch to wired to test and see if the issue goes away?
We could also have you run a WinMTR test (use the US Central IP 24.105.62.129). Make sure to leave the test running in the background while you play, and once you experience the issue wait a minute or so then stop the test.
Hit the Copy to Text button and then paste the results here so we can take a look. To make it easier to read and to allow links, highlight the whole thing and hit the </> button before submitting the reply.