Repairing AP's plastic jewellery

I haven't actually been an active lolita for a while, but one of my most prized pieces of my collection was AP's tricky night headband which I just broke on a night out. (On one of the few rare occasions I actually decided to wear it because I was afraid of precisely this happening!) 

I was wondering whether any of you have tips for the very best way to repair plastic jewellery? One of the wings of the bat has snapped off so it's in a pretty vulnerable spot and I'm not sure whether regular super glue is gonna cut it. 

Any advice would be hugely appreciated as it's quite a sentimental item!