On the article that I read (link is below), it is estimated that by the year 2140 all bitcoins will be mined out. Although it may sound that bitcoin will have its inevitable death, that will not be the case. If all bitcoins are mined out, then the price will increase and mining fees would increase as time passes by. Not to mention, bitcoin protocol also provides transaction fees which will be utilized by most miners.
Do note that what determines the price of bitcoin is the law of demand and supply. Assuming that all have been mined out, then expect the prices to skyrocket in the market, which will be an opportunity for most people who hoard or keep their coins safely in their wallet.
Link: https://99bitcoins.com/what-will-happen-when-all-bitcoins-are-mined/