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

[pumpkinpony]

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?

With USAA - they totaled our vehicle, wrote a check.. We kept said vehicle, had to put a salvage title on it, and dropped the insurance to liability only. They are only going to pay out on a vehicle once.

Oddly enough though, if you switch companies, you can probably put full coverage on it again. I had a truck I switched to USAA with a previous salvage title, and they let me do full coverage on it.