Year 2140 is when issuance will stop. So we have more than 100 years left: https://en.bitcoin.it/wiki/Controlled_supply

Beside that, transaction fees should make mining profitable for ever, in theory. Transaction fees, or transaction volume, only needs to grow by 10x in the next 10 years (from ~0.3 to 3 BTC per block), in order to make them generate more profits to miners than coin issuance.

I don't think it stops issuing coins, I think the reward keeps halving until it reaches zero (beyond 8 decimals).

The question is are people going to bother to use $10k gigahash machines with dollars/day in power to make 0.0000001 BTC

If the reward gets low enough that people stop mining, then the network adapts to make mining easier, keeping the mining rate constant. It's brilliant.

Transaction fees.