The GW2 API can return a lot of data, especially on the inventory and bank pages if you have a lot of bags / materials in storage. This can result in it occasionally getting confused and/or stuck.

If this happens to you (or you're not seeing updates) you can try the following.

On the settings page, there is a "Clear Cache" button:

Simply click that button, and then pull-to-refresh the page you're having trouble with. That should clear up the issue.