'What does happen when the chip reaches the 1000 burn limit anyways?'

Hallo Sushil,

you must think about this topic in terms of statistics. Burn limit tells you, that under certain well defined (but not neccessarily published) conditions after 1000 burns a certain percentage (e.g. 5%) of DUTs fail in becoming programmed correctly. Mostly, there is somewhere one cell in code memory which does not keep correct data. Then, program runs ill.
When I remember correctly for ATMEL chips specifications are given at 50°C tempereature of environment. When chip is running at much colder temperatures, burn limit is far beyond 1000 cycles.
Burn limit specification does only tell you, that code memory should not be changed as often as content of a classical EEPROM, e.g. But it doesn't tell you anything concrete about the chip you hold in hands. If you are lucky, you can program your code memory 10000 times. But may be, that already after 100 times your chip is damaged. Both cases are rather unprobable, but NOT impossible. Always keep in mind, that topic has to be analyzed in terms of statistics.

To your failure:
I remember an errata sheet of INTEL, telling something about same failure. There was a reset problem. Reset mode is improperly invoked. Means, that after reseting microcontroller chip does not run correctly, but hangs. Because of internal misrunning certain internal circuitry is shortcircuited, resulting in tremendous heating, possibly up to destruction. In this sheet it is advised to guarantee two different things:

1. Vcc rise time during power-up should me minimized. Power-up time of only a few miliseconds is highly recommended.

2. At power-up, reset signal at RESET pin must be identical to Vcc. So, a good reset circuit, working from Vcc=1V on and/or additional pull-up resistor of about 10kOhm at RESET pin is recommended.
When I remember correctly MAX810L with additional pullup resistor, as recommended in datasheet, works from Vcc=0V on.

Good luck,
Kai