If the new chain gets, say, 1% of the hashing power, then blocks will be found on average 100 times less often, which extends the time to reaching a new adjustment period from two weeks to 200 weeks...enough to arguably kill it.
It seems like this sort of "make the adjustment period take a horrifically long time to reach" effect only happens if the cutover is very abrupt and includes the overwhelming majority of hashpower, and if people are persuaded enough of the outcome of the fork that they don't speculatively bring new hashpower online to take advantage of the suddenly-easier-to-earn block rewards.