Just get another... in San Diego, they should be fairly inexpensive and you can try again... but look carefully for gophers.. maybe put chicken wire around the root ball this time. Grown many a Bismarckia and have not lost one yet... pretty hard to kill, though they hate being transplanted.

The pup will probably generate more pups, but the part that died is probably gone for good.

If you went from a 9 1/4" pot to a 12", that's large enough for now. I'd be more worried about over watering with the soil type you have. i have a 6 foot f. benjamina that's in similar soil (not moisture control though). since the best time to repot would be around June, I've had to leave it that soil for the winter. But I've drilled a few hundred holes all over the sides of the pot, propped it up a few inches off the ground and installed wicks into the soil to help drain perched water (thanks to Al for all of that). Just saying, there are things that can be done to "get away" with that type of soil until a full repot can be done with correct soil at the right time of year. if the plant has spider mites, you'll see tiny brown, black or red specks. Look to see if they move. If the infestation is severe, check all other plants too. Spraying weekly with a 50/50 water / 70% isopropyl alcohol mix should at least keep their numbers down. But you have to really drench all of the fronds, top and bottom along with stems. Lastly, about the light, I know you say it receives direct and indirect sunlight, but as mentioned, if the plant is not directly in front of that southern window, it's most certainly not recieving enough light.

"I water it probably once a week" Try not to water on a set schedule-water when the plant needs it. There are many ways to tell when a plant needs watering-one commonly used is the wooden dowel method. Take a wooden dowel or chopstick, stick it all the way into the soil, wait ten minutes, then pull it out. If the dowel is dirty/dark/obviously wet, withhold watering. If the dowel is clean/normal colored/obviously dry, water. "but I don't water it a lot each time" Is the soil pulling away from the edges of the pot? Peat-based soils like MG have a bad tendency to become water repelling if left to dry for too long. They can harden to the consistency of a brick. Any water the grower gives will simply run over the top, down the sides of the dry root ball, and out the drainage hole. If this is happening, then I would take a bucket or a large sink big enough to fit the pot, fill the bucket or sink to the top, then slowly submerge the pot. Bubbles will begin flowing from the soil-this is just stale air in the root system being forced out of the dry soil by the fresh water pouring in. Hold it there for a few minutes, maybe five minutes after bubbling stops to ensure the entire root ball is saturated. I would then lift the pot, let it drain well, then set it back in its usual place. "I purchased some palm tree spikes, broke one up, and put it in the pot." I've read on Gardenweb that many people don't recommend the spikes because they may cause a large concentration of fertilizer salts in one area without properly spreading throughout the root system. I would take out the spikes and switch to a 3:1:2 ratio fertilizer, like Foliage Pro 9-3-6 or MG 12-4-8/ 24-8-16. Be sure to flush the pot before fertilizing-first saturate the entire root ball, wait for maybe ten minutes, then slowly pour water so that an amount of water equal to 10 times the volume of the container exits the drainage hole. Good luck! Also, word of advice-the next time you prune something or otherwise use tools to create a wound in the plant (like a cut, etc.) sterilize the tools beforehand. You can use rubbing alcohol-wipe the blades thoroughly or soak the blades for a few minutes, then let dry. This can lower the risk of introducing infectious agents into the plant because of your cut. It may seem unnecessary, but it certainly doesn't hurt.