You can permanently modify your radio wiring per the attached diagram in order to maintain memory with the vehicle battery removed. Added components and wiring are shown in green. Diode D1 keeps the added battery from feeding back into the rest of the vehicle electrical system. Diode D2 protects the added memory retention battery from the vehicle electrical system. (WARNING! BATTERIES CAN EXPLODE WHEN SUBJECTED TO EXTERNAL POWER SOURCES.)
It is best to modify the radio memory hold wire, if your radio has one. Most aftermarket radios are so equipped. I believe most newer (since mid-1980's ? ) auto factory radios also have a separate memory hold wire. Consult your vehicle's wiring manual or after market radio information to make sure. If you can use the separate memory retention wire, the diodes won't have to handle the full radio power requirements.
IMPORTANT: USE ONLY DOIDES THAT ARE RATED FOR YOUR RADIO'S POWER CONSUMPTION NEEDS. DOIDES MUST BE RATED AT LEAST 15 VOLTS AND THE NECESSARY WATTAGE/AMPERAGE FOR YOUR RADIO REQUIREMENTS. This is especially critical if your radio does not have a memory retention wire and it is necessary to modify the radio main power wire.
If you do not have some electronic experience, it would be best to have someone who does, or an audio shop, make this modification.
WARNING. COMPONENTS THAT ARE THE WRONG RATING, OR WHICH ARE INSTALLED INCORRECTLY (DIODE POLARITY IS CRITICAL) CAN FAIL AND CAUSE A FIRE, DAMAGE TO ELECTRICAL EQUIPMENT AND/OR PERSONAL INJURY.
Scared? Well, you should be.
I would also suggest removing the added battery from the circuit when not needed. Good luck.
Memory Hold Diagram