High Voltage applied to TVS diode
TVS diodes are not capable of handling some hundreds of volts for
  30-45seconds but they can handle kV range for few micro or
  milliseconds. Why is that?


As with all use examples of TVS diodes, they are trying to fight-off a surge of current. They cannot fight against a solid voltage source because if you applied one there would be theoretically tens of thousands of amps. So, the voltage source they "fight-against" is not a true voltage source because it has series impedance. It doesn't matter whether the surge is indirect lightning or ESD - there is a series impedance that limits the current and the TVS takes this current and clamps the voltage to a peak or limiting value.

However, it will only do this for a certain length of time before the internal temperature of the junction gets too hot and it melts.

Surges are limited in time to a few hundred micro seconds so why should a TVS diode be designed to fight-off a surge that lasted several seconds?


  And why did the current draw was high till I replaced the TVS? The TVS
  was a short circuit impedance path for the current?


Because the internals of the TVS melted and it turned into a good conductive blob of semiconductor material. 


  If the TVS diode was the only problem, why did my LDO output (5V) also
  show a short circuit?


Look at the data sheet: -



The TVS might have allowed a voltage as high as 49.9 volts or maybe 64.3 volts when you applied the 130 volt supply. It might even of allowed a higher voltage - it all depends on how much current the 130 volt supply can muster.

Is your LDO capable of withstanding 50 volts?



How hot will it get

The device weighs 0.11 grams and lets say it is subjected to a terminal voltage of 50 volts at 12 amps for 10 seconds. The power is 600 watts and the energy is 6,000 joules. Now consider a material that has a really good specific heat. I'm thinking water and water has a specific heat of 4.186 joules per gram per degC. In other words, if you apply a heat of 4.186 joules to 1 gram of water it will warm 1 degC.

So, with 600 joules applied, 1 gram of water will warm 143.3 degC and 0.11 gram of water would warm by 1303 degC.

Do you see why a small 0.11 gram TVS diode will turn to a molten blob in a few seconds. Once it's got past 600 degC it's done for. The specific heat of silicon os only 0.7 joules per gram per degree Celsius so it would likely melt in less than a second.