Car got crunched; insurance company wants to say it's a total loss?

[Biciclista]

Apologize in advance for the minor hijack here...but this got me thinking, and I'm curious....
If a car is deemed "totaled" by your insurance company, and you take the check and get the car repaired and back on the road...can you get insurance for it, or will the insurance company(s) deny you?

Yes. The first time my Honda was totaled (someone stole the door off it)
I kept the title and took the money and bought a used door and went on driving it.

Since my car's being totaled didn't actually have structural damage, we didn't have to have it reinspected.