How can Magikarp die?
Solution 1:
There are several events that cause your Magikarp to "retire". Not all of these involve Magikarp actually dying, but either way they force you to get a new Magikarp to train. Taken from this list, the events that force your Magikarp to retire are as follows, with the bolded events ending in Magikarps untimely demise:
Is it Treasure?: You find a Pokeball on the ground. When you go to pick it up, either its filled with many coins or it's a Voltorb that will self-destruct.
Out of Nowhere: You come across a tree with fruit. If Magikarp jumps up to grab a fruit, it will either get a massive JP boost or it'll get snatched in mid-air by a Pidgeotto.
Macho Karp: After losing a match, a scientist will come up and ask for help in an experiment. Magikarp with either gain +1 max level, or it'll evolve into Gyarados.
Hop, Skip, Whump!: If you scroll your screen to the top of the feeding pond and tap on Magikarp, it will jump out of the water. Do this enough times, and a Pidgeotto will grab it for dinner.
Adios, Gyarados!: If you tap on Magikarp enough times while it's in the feeding pond, the Everstone it's holding will break. Once it reaches level 20, it will evolve into Gyarados.