The longer your computer is accessible, the higher the chances of an intrusion. This doesn't mean dial-up access is safe. An intruder is able to enter your computer through open and accessible ports. This means you have to make sure you don't have any unnecessary open ports on your computer, and you should secure the ones that have to be open (due to services you need to run). If you make sure all your ports are closed or hidden, the length of time you are online becomes irrelevant.
