No. The rate of coin generation is fixed. The difficulty, however, is not. It increases.
Or decreases if the computational power of the network drops (granted advances in technology make that unlikely in the long term, and only minimally impactful in the short term). The difficulty self adjusts SO that the rate of coin generation remains largely fixed.
They're not independent variables, the more power you have the faster you can compute an equation to match the current difficulty, and earn more coins, it just also happens that the difficulty is self adjusting so that the rate which coins are found stays apx. = to 1 per 10 minutes. If the computational power of the network is strong enough that it's taking less than 10 minutes for someone to find a block, the difficulty rises until that is no longer true, and if the computational power of the network drops enough that it's taking more than 10 minutes for someone to find a block the difficulty drops.
Now if just 1 miner ignores your transaction that's not a big deal, but if 51% of them ignore it, your transaction never gets verified. The same algorithm that generates new blocks and rewards (now 25, used to be 50) BTC, also includes all the transaction fees of transactions codified in that block as part of the block reward. So the theory is that once the block reward itself becomes unprofitable, miners will continue to mine (since that's what codifies transactions) for the transaction fees.