The price will not be able to increase to the point that the mining block bitcoin reward itself will incentivize miners. As the mining block reward approaches zero, transaction fees will be the only way to incentivize miners. Since there will be fewer transactions, transactions won't have to provide a large fee just in order to get the transaction in the next block. The reduced transaction revenue will cause many miners to leave the network. Fewer miners will mean easier difficulty. This phenomenon stabilizes when mining is still profitable at the lower transaction revenue level.