I've been fortunate in not having any maintenance-related downtime during African safaris. One outfitter swapped out vehicles for a day, but my understanding is that it was due to scheduled maintenance. He kept his vehicles in tip-top shape.
On a European hunt some years ago, we switched between a Mitsubishi pickup and an old Lada. The Mitsubishi climbed like a mountain goat and gave us no problems. The Lada was surprisingly capable considering what it was.
We were driving up a mountain road for an afternoon spot-and-stalk when a horrible screeching sound began to emanate from the Lada's undercarriage. A cursory inspection revealed that one of the U-bolts holding the axle to the frame had sheared off and was causing the noise. The guide and I alighted at the next turn-around point and the driver went back down the valley to a nearby town to see about repairs. No problem, we just walked a couple hundred meters further up the hillside to where we would have stopped off anyway.
As it turned out, the outfitter had a friend in the town who happened to operate a machine shop. Lacking the correct replacement part, they simply made one. He met us at the pre-arranged pickup point that evening, maybe 15 minutes or so late. Again, no big deal and we had the opportunity to watch sunset turn into night from a fine mountainside vantage point.
But it made a big difference having access to an actual machinist/mechanic vs. a certified parts-changer!