Why does one of my 10s cut out when I turn it up?

That drop out sounds like a phase issue or a physical connection problem on the left side, not likely the head unit signal clipping since that usually affects both channels simultaneously. If one sub is failing at higher volume while the other runs fine, we are usually looking at a grounding problem, a bad wire, or something loose in the terminal connections of the left sub.

Start by inspecting the negative ground cable running to that left subwoofer. Even if the main power terminal looks snug, a loose or corroded ground connection can cause massive instability and audible drop outs when the amp demands high current. Try swapping the ground wire to the other sub, just to see if the behavior moves. If the problem stays on the left sub even with a new ground, then it's the driver itself.

Since you mentioned checking the terminals, verify the polarity and the tightness of every single lug at both the amp and the subwoofer. Don't just check the surface; make sure the actual wire is seated all the way into the binding post. A slightly loose connection can overheat and cause intermittent impedance changes that sound exactly like a drop out.

If the wiring and ground are solid, look closely at the physical mounting of the left driver. Sometimes the magnet or the basket can shift even slightly during a heavy bass session, affecting the voice coil dynamics. Give the driver a gentle wiggle and see if the drop out persists. Since it's new, it's possible a component inside the sub was improperly seated during manufacturing or installation, though that's rare. A quick test would be running a known clean signal, like a pure sine wave, directly to the left sub to rule out any amp output issues.

One thing that got me a couple years back with a similar symptom was the amp itself running out of steam, not the sub. If both subs share one channel and the box is ported, the impedance dip down near tuning can pull the amp's output down hard right when the volume climbs, and it can look like one driver quitting when really the whole channel is sagging. Try swapping the left and right speaker leads at the amp end, becasue if the quiet side follows the wire instead of staying with the same driver, you have your answer without pulling the trunk apart. Also worth checking wheather your head unit has a sub level control buried in its audio menu, since mine was set low by default and it made everything behave weirdly past halfway on the volume dial.

Had almost the same ghost chase in my hatchback years ago. Turned out the wire was getting pinched between the sub's basket and the box cutout when I torqued the mounting screws down. Played fine at low volume, then cone excursion would pull the strand apart and it'd fade out. A cheap multimeter with the continuity beeper found it in two minutes while wiggling the wire by hand. Pull that left driver and check what's underneath it before you suspect the coil, it's a five minute job and it saved me from returning a perfectly good sub.

Update: the pinched wire comment got me thinking, so I pulled the left sub out tonight and sure enought the wire runs tight along the bottom of the cutout. Haven't found a pinch yet but I did try pushing the cone in gently by hand and it crackles sometimes. Would that show up on a multimeter too, or is a crackle at rest a different problem from the fading at volume?