I have been told that NE 1 House of period 8, is lucky for this period only and not lucky in period 9. Is it so?
If so then could some one tell me the reason for the same.

A period 8 NE1 facing house has the 8water star in the facing palace... which can be good.
But in period 9 it is retreating qi and of little use.

That doesn't make it a bad house... its just that it can no longer benefit from having the current yun star in the facing.
There are many other factors...surroundings, qi flow, whether the main door is in NE1, etc.... that may prove more important to the luck of the residents

Presently the door is in the NE sector and facing NE1. To have a better luck, would I have to change it to some other sector?

If you are living in a P8 NE1 facing house you have the 8 water star at your Main Door.
Popular feng shui would say that there is nothing luckier, and since your main door is there, no further activation will accomplish anything (unless you don't really use that door!)

So a more thorough audit of the surroundings, the internal qi flow, etc. would be needed IMO to understand why you are not doing well. Then some choices to improve things could be figured out.