A lot of great items for execution and operational challenges are already listed so to add to the conversation I'll focus a little more on the business strategy.
If you look at the auto repair business (mechanical, paint, etc.) the business models are similar in the general strategy. They attempt to streamline the processes or areas of expertise. Diagnose, repair, repeat. The goal is to just like a restaurant in a lot of ways. The more turn over they can manage in a given period the more revenue they can bring in. Streamlining the process can help control costs, reduce process time, and increase the bottom line / allows them to operate in the black. The best general managers / owners are the ones who can manage to the model and manage the execution/operational challenges already listed.
The business model for a custom car shop is by it's nature an inefficient processes. Each car is a one-off build requiring multiple sets of talents (metal fab, paint/body, wiring, plumbing, interior, engine/mechanical). As your business becomes more specialized or less streamlined your costs increase which drives up your prices. If a auto repair hourly rate is at $110-$140 having already built in the efficiencies into the rates then your custom car shop would be much higher. This rate is a basic calculation: Annual (Overhead (rent/insurance/etc) + labor + parts + marketing/advertizing + unexpected overage ratio + profit percent) / (Number of units (cars) per year). With your cost per car baseline you can then figure out your hourly rate by dividing your available labor hours by number of units per year, then divide it by the cost per car.
Many of the successful shops I believe started on a shoestring approach with one or two people who had a wide variety of talent sets required. As they were able to build a customer base they quickly compartmentalized the build process as quickly as possible to streamline and reduce build time. You see this with many of the successful shops though you may not recognize it. There are designated areas and resources for each step of the process.
I believe many of the unsuccessful shops failed because they never moved beyond one or two people trying to do everything. If you are a two man shop your cost per hour has to be extremely high in order to break even and keep your doors open. As a customer, would you pay double the rate of a national know/name build shop to support your local builder with 2 resources? Probably not. The only caveat here I can think of is the retired/hobby shop owner who does it out of 'fun' with the sole purpose of trying to stay out of the red at the end of the year while having fun in the process.
As a business model the custom car shop is something you really would never want to invest in. The most successful shop isn't going to bring in more than a few million at most for the owner, it's not replicable (you can't easily franchise or open multiple locations due to the highly skilled talent required), and the market of people who want a custom car is very small and of those who can afford it it's even smaller.
Hat tip to this thread being started.