Low amp draw from battery?

Bit more of an electrician question I think, but here goes.

I have a battery that "should" work with up to 30 amps. I have a radio AND a raspberry pi (with a monitor attached) hooked up to the battery. The radio only uses about 9 amps when transmitting, and the pi idles at about 1.5 amp, but needs about 3 amps to comfortably run the screen too. So, at most, I should only be pulling about 12ish amps (plenty of headroom).

The trouble is, when I start transmitting, my pi isn't getting enough amps (it drops to about .9 amps), which causes the screen to turn off. The pi and the radio are hooked up to the same battery in parallel. Is there some kind of ramp-up time for a battery to give the amps it needs? Is there a better way to hook multiple devices up to a battery? Or is my battery just garbage? I appreciate the help!