Why does my voice shake when I hold a note?
Other reasons for shakiness
Vibrato is a skill that must be developed on it's own, after a singer can comfortably hold a note for a few seconds at least. Sometimes a singer is trying to hold a note that holds a bit longer than the notes around it. Because a singer hasn't developed their steadiness, they start to shake.
How long should you be able to hold a note?
On a low note, probably 30 seconds. In my lower range, probably past 20 seconds. but as you get higher I find you can hold the note longer by making it softer. That way you aren't forcing too much air out with the note but just enough to hear it and you will notice you can hold it a lot longer.