You are forgetting that Bitcoin has transaction fees. The total sum of transaction fees paid for transactions in a certain block goes to the miners solving that block (in addition to the block reward). While total transaction fees today are typically significantly less than 1 BTC per block, this total sum is already significantly higher than a few years ago.
In future, transaction fees will progressively increase in relevance compared to block rewards and ultimately entirely replace them as an incentive to solve more blocks.
You also have to consider that with decreasing block rewards, Bitcoin's valuation will very likely increase significantly. So mining might still be profitable, even if the amount of Bitcoin obtained in the process is only a fraction of what it is today.
ya.ya.yo!
I've read through all the comments and I think this is the best explanation. It is simple yet very informative.
To sum up all the comments which make sense to me: Yes, Bitcoin is designed to last forever.