You're ok if the first 3-4 threads are engaged. This is where most (roughly 90%) of a threads holding power is, even on deeper engagements. Ideally, you want minimally 1-2 threads showing past the nut. This is the standard minimum for bolted connections in the industrial world.

Also, is it a new axle? and are the thread engagements the same on the other side? If it's short on both sides, methinks that maybe they installed a bolted track axle on a road width hub, since it's a conversion. In other words, the axle is too short by ~3mm on each side.