Why does my old amp keep going into protect mode when I turn it up?

The cycling you are experiencing is almost certainly a thermal shutdown, given the placement under a shelf in the trunk, especally when running gear from that era. Those older units were often designed with smaller heat sinks and didn't have the sophisticated thermal management found in modern electronics. Being under a shelf means you are essentially creating a heat trap, and the amp is hitting its safety threshold when the current draw gets high enought to generate critical heat. Standing it on edge might help a little, but you need actual clearance and ideally, some forced airflow directed across the unit. As for your concern about impedance and wiring, while that could contribute, the immediate shutdown behavior screams heat first. Check the amp's specifications again to confirm the required load. If the sub box wiring is too low (like a momentary drop to 0.5 ohms when it's rated for 1 ohm), the amp's protection circuit will trip, which mimics thermal issues, but you need to confirm that the load stays constant across all frequencies. If the load is correct, then heat is the dominant factor. You should try moving the amp to a spot that allows at least 4 inches of clear space around all sides, and if possable, elevate it off any surrounding plastic or metal that might be absorbing heat. If moving it drastically changes the cycling point, you know heat was the issue. If it still cycles, then you need to test the power input. Even with thicker wires, a sudden voltage sag under heavy load can trigger protection on sensitive older amps. Grab a multimeter and measure the voltage right at the amp's terminals while you are pushing the dial to that shutdown spot. If the voltage dips below the amp's required minimum, you have a power delivery problem upstream.

Since you want to keep the gear, addressing the heat is the most immediate and necessary fix. The retro sound is amazing, but if it's tripping protection, you're not enjoying the sound it's capable of.

I have those big batteries under the seats, and they feel really heavy and old. Since everyone is talking about the heat and the wires, I was wondering if the batteries themselves could just be tired and not giving enough power when I crank up the volume. My radio always starts acting wierd when I push it hard. Do you think the batteries could be the reason the amp keeps shutting down, or is that just the age of the electronics?

I think you need to check your connections. Sometimes the protection trips not because the amp is too hot, but because a bad connection is creating a massive power sag under load. When I was fixing a similar unit a while back, I used a simple torque wrench on all the binding posts, and it completely solved the cycling issue. Those resistance spikes from loose terminals act just like a short circuit to the internal safety circuits. A tight bond is often the simplest fix you can find, especially on gear that is this old. Check all the terminals from the battery down to the amp input.

I keep getting confused because my setup is also older, and it's hard to tell if it's a simple wiring thing or just the age of the parts. The others keep pointing at the heat, but since the amp is basicly bolted down, maybe it's not the ambient temperture but what the power supply is feeding it. When I push the dial hard, the amp seems to pull a huge surge that feels like too much for the factory wiring to handle without a drop. Do you think the amp is just tripping because the power delivery itself is too weak under that sudden load?

I relly think claiming the cycling screams heat first is jumping ahead. While heat is definately a factor with older gear, a sharp shutdown like that often points to somthing being more fundamental than a thermal trip. When I worked on a similar setup, the amp would just cut out precisely when the load was pushed, wich is ussually when the power delivery starts to fail.

It isn't always a heat issue; it's frequently a voltage drop problem. The amp might not be hot enough yet, but if the power supply simply can't push the required amps under that stress, the protection circuit trips regardless of temperature. I’d start by checking the voltage right at the amp's terminals before concluding the heat sink is the culprit.