High current draw causes 7808CT Regulator to shutdown?

Well, some RC ESCs use parallel 7805s without any problem.

Update: realised that the Nicd battery caused the sudden shutdown through the voltage regulator. If the voltage regulator was not used, the system can be powered optimumly with direct battery. However, due to the fact that i still need it to produce 8v linear. Therefore, i have managed to use a dc to dc buck converter connected to a power supply for my project. Though there we still some doubts on why the battery paired with the regulator/buck converter would cause reboot during higher current draw situation :confused:

You do not seem to fully understand some important properties of such batteries.
A battery has an internal resistance.
That means it has an unintentionally built in current limiter.

However, the < 1 A maximum you measured might not be enough for this to really cause that problem but that depends again on exactly what battery was used.