Sidewall repeatedly splitting in same place on rim
Mark and note where the split happens on the rim. It's possible that the fault on the rim is only discoverable when the tyre is inflated. Perhaps, there is a crack in the rim. If you have a pair of callipers, measure the width of the rim with the tyre inflated and uninflated. This may highlight such a crack/failure.

Also check the geometry of the wheel by slowly turning it and examining the rim at the brake block as it rotates.

If either of these tests show problems, the rim should be replaced