Yes, I've mostly shot animals with the .416 Rigby multiple times. This is because all the animals I've shot with it have been either Cape or water buffalo, and the standard procedure with either is to keep shooting until they lie down and stay down.
Sometimes a buffalo will disappear into cover after the first shot without a chance for a second shot. If it was shot well, then it will go down within 100 yards or even less. Even them, it's SOP to shoot them again after you find them. In Africa this is sometimes called paying the insurance, since "dead" Cape buffalo have been known to get up and stomp people.
Buffalo are big and tough, but in general I haven't found African plains game to be any tougher than North American animals. Before going further, I should note that to most hunters, "tough to kill" generally means hits around the edges of the vitals resulting in the animal taking off and going a long way.
Blue wildebeest have the reputation of being perhaps the toughest of plains game, but I don't think they're any harder to kill than elk. Most of the wildebeest I've seen taken have keeled over within 75 yards from one shot, and the cartridges used have included the .270 Winchester and 7mm-08 Remington. Like elk, if you shoot wildebeest in the right place with a bullet that penetrates and expands sufficently they will soon be very dead.
If you don't shoot wildebeest in the right place, like elk they will go a long ways. Probably due to coincidence, the wildebeest that I've see go a long ways were all shot around the edges with larger cartridges, one reason I tend to doubt the claim that bigger cartridges can make a difference on "marginal" shots. (Finn Aagaard said he thought bigger cartridges might make a difference in a shot an inch or two off, but not on real mis-hits. I agree.)
Gemsbok and zebra also have a reputation for being very tough, but Eileen dropped her gemsbok neatly with one 165-grain bullets from a .30-06. She did shoot a zebra twice with 150's from a .308, but the second shot wasn't necessary. Her PH was telling her not to shoot, as the zebra was about to go down, but she tends to keep shooting until everything stops. Both animals were big trophy males, by the way.
I haven't found any of the smaller African game to be any tougher than pronghorn or a rutting whitetail. Eland are no tougher than moose. I could go on and on with other examples.
I do suspect that some of the reputation African game has acquired the reputation of being extra tough is due to bullets that might be tougher than they need to be. One of the quickest kills I've seen on blue wildebeest was from a 140-grain AccuBond shot from a 7mm-08. The hunter put it through both lungs right behind the shoulder. The bull started running but keeled over before the hunter could shoot again.
On the other hand, an African safari usually involves animals of very different sizes, and it's smart to use a bullet that will penetrate the largest the hunter might encounter. Another companion once shot a zebra with the "light game" bullet from his rifle, chambered for one of the short magnums, and the bullet only penetrated one lung. He and his PH eventually got the zebra, but only after a very long afternoon. The PH told him not to use that bullet again.
In general I prefer bullets that result in more internal internal damage than some of the super-penetrating bullets available today. The Nosler Partition has never let me down in Africa (or for that matter, anywhere else) whether on plains game or buffalo, though it should also be pointed out that the bigger Partitions (say from the 250-grain .338 up) have the partition moved forward to retain a higher percentage of their weight.
Eileen and I have killed a pile of deer with the 150 Nosler Partition, along with elk and her one bull moose. It has always killed quickly and penetrated plenty. Power Points are good bullets, but don't kill any quicker than equivalent Partitions and don't penetrate as deeply. If you might take the occasional angling shot the 150 Partition would be an excellent choice for deer and pigs.