I have the official Teclast stylus, and so far it’s working great.
Lately, I’ve been having serious battery issues.
Put in a new batter last week, used the stylus only once and put it back to the laptop’s bag. Took it out now and it’s completely dead. I had to change to a new battery to get it to work.
I though there’s a sleep mode for the stylus, maybe mine’s broken.
My batteries work for around 2-3 month with average usage. However I think that the pen discharges batteries relatively quick when not using the pen for some time (might be the batteries themselves aswell). You could try different batteries or try removing the batteries when not using the pen for some time.