typically is fused at main fuse and the battery at 20 amps. If the fuse size is less than 15 amps you could be under fused. Since the fuses aren't blowing right away it's not a dead short. Here's what I would do.
1. Check the sizes of the main fuse and the one at the battery. (20 amp is normal)
2. Go to the converter and remove all fuses.
3. Get a current meter. Most Digital Multimeters have a current range. Make sure it will handle around 40 amps or more amps. An inexpensive one can be purchased at any Radio Shack, automototive parts, etc. Place the current meter in the power line. At the battery is probably the best place. With everything off and the fuses at the converter pulled the current should read 0.
4. Replace the fuses one at a time and check the current. Without turning anything on the current should still remain 0.
5. Start turning stuff on, one a time, and checking current. There should be some current depending on what is turned on. Turn each item back off before turning on the next.
6. If you haven't found something by this time that's drawing more current than 20 amps, turn on all the stuff that you would normally have on and check again.
This should tell you where the excessive current is going.
A little bit about fuses. A fuse rating is specified in amps and time. A 20 amp fuse might take a 40 amp load for 30 minutes. A 100 amp load would blow the fuse almost immediately. A 25 Amp load on a 20 Amp fuse could take weeks to blow, or may never blow. That's the nature of fuses and circuit brakers.