The question is: How high will the transaction rate have to be to incentivise enough miners to keep the network secure?
Or: How low can the difficulty fall for the network to be considered secure?
It won't be a problem because the number of minors won't change suddenly. While a drop of 50% in the block reward seems like a lot, it really isn't, because it's the some order of magnitude. It would be a big drop if it happened without warning, but minors plan their purchases will in advance.
A 50% drop in block reward means a 50% drop in mining revenue, assuming everything else stays the same (transactions fees and the BTC exchange rate), which in theory could mean a 50% drop in the number of minors. At that number, the network would still be considered secure, based on the current numbers.
Today, the block reward is half what is was 4 years ago. The BTC exchange rate, however, is much more that twice what it was. I believe that statement will be true for decades to come. Thus, there will always be enough minors.