Once the dropship I've created loses a engine, it tends to just blow up even though still has at least a few hundred health remaining. What could I do fix this?

increase the gibwound limit

Or perhaps the GibImpulse limit. If the engine gibs into any particals, then increase the gibwoundlimit aswell.

The exploding is most likely cause by a gib of the engine hitting the hull hard enough to gib it. Gibimpulse determines the size of the imapct the object can take before it gibs.