Are you running the inverter from your cigarette lighter plug? You're probably running into the amperage limit of the cable running in your car up to the lighter plug.
I ran into this same problem a couple years ago. I bought the inverter right before a road trip to Vegas. On the drive out, the inverter would beep an overload warning after about twenty minutes of using the laptop, and about a minute later it would burn through the fuse.
Not wanting to go without my laptop on the drive back as well, we stopped at a Wal-Mart and bought an extension cable, roll of electrical tape, bag of zip-ties, and a handful of the cheapest and worst quality tools I've ever seen. We cut off the ends of the cable, bolted one end right to the battery terminals, ran it back under the hood, through the passenger side doorjam, under the dash and to the inverter. Then we returned the tools.
It worked beautifully.