Plying fine singles can be a challenge. For starters, I never use the Andean Plying Bracelet (unless I'm doing a fairly short length -- under 20 yards) nor a center pull ball -- both have too much opportunity to tangle.
On a wheel, I use two bobbins, on a tensioned lazy kate, several feet behind me. On a spindle, I'll pre-wind two spindle-fulls into a ball and then add the plying twist from that 2-strand ball.
If the singles are drafting apart when you ply, then I'd recommend putting more twist in your singles; this will help them stay together for plying.
If the singles are snapping when you ply, they are probably very thin and also very high twist -- the best way to stop them from snapping is to completely minimize the draw-in on your wheel down to just-barely-drawing-in when you ply. Also, I'd recommend in that case, a little less twist in the singles -- so they won't be under so much tension, this should reduce their desire to snap on you during plying.
(based on a post by me on Spin to Knit Socks, May 07)