That's the whole point. As the amount of Bitcoins gets closer to the maxim, it will become harder and harder to mine them. But ideally, this should be overcome by Bitcoin's increasing popularity and value.

This isn't happening right now, and it appears to have stagnated, but that's not a problem for Bitcoin's future, because the continous mining of Bitcoin is not necessary to ensure its success.

This simply means that there has to be a bigger real economy behind Bitcoin's value, and once that economy is strong enough and catches up with Bitcoin's inflated value, the value should start rising again, and miners will appear again as it becomes profitable to mine them.

It doesn't matter how many people are mining, coins are generated at a fixed rate. The difficulty to mine coins is varied automatically to assure this.

It's this difficulty that affects miners when more folks start mining. In effect they are taking the known portion of the pie (coins to be mined in a given time frame) and slicing it into many more pieces. This means that you have to work for a much longer time to have a nice large piece of pie with plenty of room for ice cream and whipped cream on top.

Isn't the expectation that the miners will compete to confirm transactions, and there is an expectation they will work for small transaction fees?

Except if Bitcoin becomes popular, other similar digital currencies will arise. Bitcoin will be no more speicial than nickels are in the non-digital currency realm. It will be just another kind of digital coin in your digital pocket.

Beyond a certain point the majority of the mining reward will come from transaction fees.