Will it be profitable for bitcoin miners once all bitcoins are mined?

In theory-yes it will be profitable for bitcoin miners to mine even with all the bitcoin mined. There are 3 main way how:

• Mass Adoption
  You see miners also get paid in fees. When Bitcoin blasts off and the world adopts bitcoin -the value of bitcoin will also increase. As such say miners earn 0.1 btc in fees today which is $70. But in the future 0.1 btc can be worth over $600. Get the idea? The fees will pay for itself!
• Efficieny
  As you can see Bitcoin machines are getting cheap and cheap to run by the day. In fact. even with the price dump with the lastest machine you can make profit! And in theory bitcoin mining can use remmenable cheap energy which will make bitcoin mining even more profitable.
• Sidechains+Merged mining
  Side Chains are separate chains that connect to the main net. Merged mining can be done with side chains. The most famous merged mining sidechain is RSK an Ethereum based sidechain aka a sidechain that can do smart contracts with 100K tps.
  With giving more use to bitcoin, miners can earn even more money in fees.
  Another way to merge mine is merged mining bitcoin. You can merge mine Namecoin with Bitcoin. Dogecoin can be merged mine with Litecoin.

You should worry about Bitcoin mining be profitable. It always will be. What you should care about is how much adoption bitcoin gets. As you can see from this bear market, when Bitcoin falls so will ever other altcoin. Love Bitcoin as much as you love your altcoins. :)