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?
You may want to learn more about mining difficulty
In fact, this question has been asked and answered infinite number of times already. It could be said that it has been beaten to death by now (maybe, that's why it is constantly asked all over again). If current generation of miners decide to leave (for whatever reason, not necessarily due to their revenues declining), the mining difficulty will adjust soon thereafter, and it will be profitable to mine bitcoins again. And it will adjust all the way down to mining starting to be feasible on GPU or CPU, as it had been at the dawn of the Bitcoin era