It depends on how you are trying to restart the calculation and why it failed.
If you want to restart the calculation from a checkpoint file, it wouldn't make sense to restart a single point energy, as this kind of restart doesn't actually pick off at the precise moment the previous calculation failed.
If you want to restart the calculation with the appropriately named "restart" keyword, it could be done in theory, but for one requires a specific setup of the calculation, and secondly can only be restarted in certain cases. Any calculation which failed due to an error requiring user intervention for instance could not be restarted.
Simon Janich and Subhasish Mallick, thank you so much sirs for your thoughts about this. Sorry for not making it clear why I considered to do a restart in the first place.
The mere reason for my case is power interruptions. As unfortunate as it may be, unannounced power interruptions occur in my place and inevitably, the machines turn off and calculations are terminated abnormally. There were no error messages whatsoever, nevertheless.
I was able to do restart using both chk and rwf files as advised in the gaussian website but I notice that for single point calculation (using MP4/6-311G(2d,p) for example), the restart proceeds quite slow. I'm wondering if it has something to do with the program itself of maybe this is mainly because of the huge basis set I'm using.
There is a number of factors which can play a role here (size of the system you are calculating, the hardware, and how the calculation is setup - i.e. how many CPU cores and memory it uses), but in general you can expect a MP4 calculation to take quite a while.