Help my car stereo has a problem please read?
It probably has a power distribution system built into it. As you well know, cars need alot of power to get the engine started, thus putting a load on your battery.
Some systems like your radio have software that allow them to start/turn on, using the least possible power.
Remember, if it gets worse, THE LAW IS ON YOUR SIDE,the Sale of Goods Act makes it obligatory for any mechanical or electrical fault to be repaired free of charge by the seller if they occur within the first 28 days, or else refund the purchaser if this is not possible. 'Sold as seen' is meaningless in UK law, and the product for sale must still be fit for purpose - stick 'sold as seen' into Google if you don't believe me.
Have a good day...