1999 Honda Accord difficult starting

Hello, I have had my 99 Honda Accord V6 since 2002. I purchased it, used, with 50k miles on it. Until now, it has performed flawlessly, and has never let me down. Here is the problem, which has occurred with sudden onset. When attempting to start, hot or cold, the starter will turn the engine over and over but the ignition will not "catch". Sometimes, when this is happeniing, if you remove and reinsert the key to try again, the engine will start, but sometimes not. And you will drain the battery continuing this. I was wondering if the problem is somehow related to the key, ignition switch, theft resistance system, etc. Any ideas?