The problem is likely with the wiper motor's park mechanism. This is a small gear or other component within the wiper motor that's responsible for positioning the wipers correctly when they're turned off. It's either broken or malfunctioning.
You might also want to check the linkage connecting the motor to the wiper arms for any damage or binding.
Replacing the wiper motor is the most likely solution, though a skilled mechanic might be able to repair the park mechanism if it's a simple fix. Replacing a fuse won't solve the issue.