Why would the girls be in trouble if the warp thread snapped?

I know that the question asks about the "warp" thread, but I am concerned that it might be asking about the "weft" thread. The two words are a bit similar, and they both are very related to the weaving that Lyddie was doing. Additionally, the girls could be in trouble (for different reasons) if either of them broke.
The warp threads are the up/down vertical threads that the weft thread gets woven through in a back and forth (left/right) motion. I'll start broad, and work toward more specific trouble for the girls. If either the warp or the weft breaks, the machine must be stopped in order for the girl to fix the break. The result is that a particular girl's productivity is slowed down to fix the break. This affects the factory's bottom dollar. Slower production means less profit. A girl that repeatedly has broken weft or warp threads is in trouble because she isn't earning what the factory wants/needs. She could lose her job. Mr. Marsden even tells the girls this.

If you can't do the work, . . . there's many a girl who can and will.

A broken weft thread could cause trouble of a different kind for the girls. A broken weft could injure a girl. The weft thread is attached to the shuttle, which is flying back and forth quite quickly. The shuttle could fly off of the machine, hit a girl, and deal a serious injury. This is exactly what happens to Lyddie in chapter 13.