What's confusing you is howe the power increase (P= I^2*R) is occuring. If the resistance increases without the current decreasing, the power will rise. Of course, the only way this can occur is for the source voltage to rise exponentially.
In your example, when resistance increases (with a constant voltage), the current must fall, so the power cannot rise. In "P= I^2*R", you're attempting to keep the current constant as you increase the resistance. It can't happen that way.
When juggling formulae, you have to remember which of your parameters are variable and which are not. In real world claculations, we generally consider that the source voltage and the equipment resistance are constants, and calculate current and power.
(Edited to repair tired-finger spelling errors)
[This message has been edited by Larry Fine (edited 09-18-2006).]