I realize the fuse in the panel calls for a 10 amp.But the question is what fuse does your new stereo call for? You say there is another fuse behind the stereo that does not blow? How many amp is that?
I'll explain why. If your stereo draws 20 amps and the fuse in the panel is 10 amp, it will evenutally heat up and blow. Its like the fuses in your house....one may be a 15 amp but if you hook up appliances that draw 20 or 30 or 40 amps the 15 amp fuse will blow. It does this for safety.
If your stereo is made to run off a 10 amp fuse and the fuse behind the stero is 10 amp then I would say the problem is something else. If its is something else it is being triggered by something your are missing. Something is happening at the instant your fuse blows. For example, the stereo works fine then something happens where the car draws more power or send power to something that causes the fuse to blow. You may not notice it...it could be as simple as you turning your headlights on or your windshield wipers on. If its is something else you need to make the fuse blow. Its trial and error...test the various circuits. Start the car, play the stero, then turn the lights on...wait....then turn the wipers on....wait...etc...etc..
Jim