What everyone has posted is true. Along with that, upgrading the fuse upfront should solve your issue as long as you have the relay wired up correctly.
Efficiency in a DC environment is always an enemy. Much more so then in AC because the voltage/current ratio is so much greater.
Example: Let VAC=voltage alternating current (House) VDC=Voltage Direct Current(Car) A=amps and W=wattage @100%efficiency.
115vacx2a=230w and 114vacx2a=228w vs. 12vdcx25a=300w and 10vdcx25=250w
Do you see how just a 2 volt drop in dc causes such a need for increase in amperage to keep up? The use of Ohms Law can be used to verify this.
That said your 12 gauge line should be fine to run the adapter. A 15' run of 12 gauge automotive grade wire should yield a maximum safe amperage of around 20 amps @ 100% efficiency. That would be the MAXIMUM rating. Running a 10 amp or 15amp would be a safe bet.
If your unit didn't come with a fuse built in (usually either on the unit or in the head of the 12 volt adapter) look on your auto/air adapter for the power consumption rating. Whatever that is (usually written in wattage) take that and divide it by 12.5volts. That is what the minimum basic voltage typically is for an uncranked battery. The result of that calculation will be the fuse rating you want to use +10%. The 10% will account for peak on demands it may see(ie voltage spike).
Hope this helps.

I have been doing custom car audio since 1996 and haven't fried anything yet.

Good luck and post some news back.