Is the problem that it's in your queue but doesn't start researching? I figured out what the problem is for that. Say you have fleet control currently researching and you go to queue up another item after it. When you queue the new item to research, it should show up as Queue Position 1. If you tap on the new research item too many times (triple tap instead of double, or double tap after it's already selected etc), it'll try to add it to the queue again and bump up the position, so instead of being position one it'll become position 2 or 3, even though there is nothing queued in position 1. So when your current research finishes, it goes to move on to the item queued in position 1, but there's nothing there so it just stops researching. Take a look at your queue, if you see higher position numbers but no Queue: 1, remove everything and carefully readd one at a time and make sure they get the correct position number and you didn't tap too many times.