When working with Lycra, spandex or even some knit fabric and attaching elastic - needle threads break. In the past when I have had this problem, I found that lengthening the stitch really helped. Another problem believe it or not was that the needle thread tension was too loose - but just slightly. Especially when you are crossing over joined seams you need to have a long enough stitch to allow for the loft or density of the several layers you are joining. At times you can split the difference and make the stitch length a little longer than normal but not a full number.
Of course it makes a difference if you are using a 4 thread serger or a 5 thread serger(coverstitch).
And thread makes a difference. Don't use inexpensive thread for garment construction. It will give you more headaches than you can handle.
I was making my sister a pair of flannel back silk pjs and used that discount thread from the fabric store. What a mistake. There were several cuts in the thread and it was weak. By cuts I mean that I would be serging along and didn't notice that one of the threads was broken etc. What a nightmare.
Now I use Robison Anton Polyester thread for projects that are important to me. It is strong, comes in several colors and holds up well. For items that won't get a lot of wear I use the cone threads.
But I have to say that over the years I have used many different brands of thread in my serger, especially when color matching was crucial.
I am leaving for New Orleans today, hopefully I will bring back some cool ideas to share with ya'll.