A quote from my signature site: "Transactions fees may supplement, and must eventually replace, the diminishing block reward paid to miners."
It is economically uncertain if purely profit-motivated mining would maintain a sufficient difficulty against attack, however there will be holders of 20+M BTC at that time that will have an economic interest in the operation and stability of the network and may mine as part of their business interests.
Oh ok, transaction fees will supplement, that makes a lot of sense since in the hypothetical scenario we'd assume bitcoin (or whatever digital currency is the subject of interest) is a widely adopted coin on a global scale so the worth of 1 full bitcoin would probably be so immense that a miner just being paid on transactional fees will find that it's still worth it to mine. Gotcha.