As block reward decreases, miners will be dependent on transaction fees to suffice for their electricity costs. By then, if the price of Bitcoin isn't high enough, it will lead to a further reduction as miners abandon their business because of the lack of profit. Thus it could be said that Bitcoin can either do very well or collapse completely in 2140.
Doesn't the Bitcoin system fail in this way or are there any other variables in play that stop such a breakdown?
The problem is that Bitcoin did not have a cap of 21 million coins, instead the number would wrap every millennia (a new "deposit" found) and start back at 50. After Satoshi left somebody added the 21 million cap because web apps were not compatible with the wrapping mechanism of the reward variables in c/c++ (they would not wrap). So yes a Bitcion will have to be worth 1,000,000 USD by then for fees to support the mining infrastructure.