Why do Completed topics lose status overnight? As is, I'll never obtain a 2nd tree.
Completed topics degrade slowly, and doing new skills will strengthen the old ones, maintaining a fluency of around 40%. If you do a second tree, you must practice both everyday or let one just degrade...
Should I care about topics degrading? Will degraded topics prevent me from finishing the tree? I do strengthen old topics, based on what I think I need, not on their decaying status.
No, but it's best to strengthen topics from time to time. You can complete the tree without all skills being gold, but when it reads 3/5 on the strength bar next to the circle, you know it's time for a light practice. If it reads 2/5 or 1/5, you may want to spend some time on the topic. It is a good idea to strengthen what you need, but as a general rule you should practice weak topics/skills. By the way, you may want to read the article on rate of decaying in the Unofficial Wikia. If you do not use the "hints" that you get when you hover (This action is known as Peeking) , the skill will not decay as quickly. Hope this helped.
You are not required to keep skills gold. If an optional feature is helping you, use it. if it is not helping you, don't use it. Good luck with your second tree. :)