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?
I don't think the Bitcoin system will ever fail, and 2140 is a very long time to go. I feel instead it shall expand a lot whole more than that, plus the value of Bitcoin shall only go up and up never down. I am 100% sure the miners shall continue to mine their coins and they shall be profitable, no one will give up on a cash making business.