Well, it's certainly one possibility! Crimped connections are great when they work, but can fail without it being obvious to look at. If that brown wire came out without much effort, then it suggests it wasn't right.

Looks to me like you have those motors wires in parallel, as there are four connections with two motor wires to each. Disconnecting one winding would have reduced the current on that phase, but would also imbalance the load on the chip. Quite what effect that would have is beyond my experience, but who knows. Certainly something to fix though!