In short.
Caps have to draw the power in order to store them.
On a long bass note, from say Put On or something like that which is pretty consistent, that cap is going to drain while the amplifiers are still pulling juice.
You now have the amps pulling juice, as well as the cap. You are now putting a larger strain on your battery.
Buy an additional larger battery for your rears. It will help.
While that is a popular theory these days, its simply not the case. A capacitor is a storage device whose voltage is controlled by system voltage. (system voltage being the over all voltage of your charging system, be it from the batt(s), alt, etc)
In other words, the cap will only draw current to recharge once system voltage starts to rise. While the long bass note continues, system voltage stays low, so does the voltage in the cap. The cap is NOT recharging. But as the bass note subsides and the charging system catches up, system voltage rises which forces the cap to recharge. The cap(s) only recharges when the system has the extra resources to do so.
That's the good news for caps, the bad news is until the point the charging system catches up and starts to recharge the cap, the cap is just an added resistor in the circuit that creates no benefit. The argument could be made however that if this situation occurs, that bass notes outlast your cap's charge, that you simply need more capacitance... not that its a sign the idea of caps does or does not work.
That's pretty much all theory. In reality, companies have very cheap caps made, and attach even more resistors to them in the form of voltage gauges and flashing lights ...blah blah blah... to the point they most times are nothing more than trunk art.
The original person to use large external caps in car audio never intended them for a power source anyway. I dont understand why the industry fixated consumers on such a flawed understanding of caps in 12v audio, when they could have simply sold them on voodoo that surround reality... as an AC (noise) filter. Hey if its a 'filter', and you stick it on the wire just before your amp, it must be helping the amp run cleaner power right?
Oops Im rambling.