Why didn't the Saiyajins raise up their power energy? A Saiyajin can multiply his power if he takes great damage or is near death and is able to heal himself afterwards.

With that ability alone, they could rinse and repeat countless times before the first encounter with the Androids (you can't be too safe).

Goku and Vegeta have their pride and all, I get that. But Trunks and Gohan are much more rational (especially Future Trunks). So why didn't they do what Vegeta did on Namek with Dende for example?
There are multiple things against this. 


It needs a close death experience to gain power and they need to be healed afterwards, as Dende wasn't on earth at this time and they surely don't want to eat all the beans. It would take a lot of time to regain their full strength and they could die trying of course.
Vegeta and Goku would never use something like that to gain power because of their pride. 
They might have underestimated the cyborgs
Future Trunks was not in this timeline on that time
Gohan was a kid at this time and he "had to study". His mother would have never allowed him to be beaten half dead and recovered just to increase power.



   6. Future Trunks might not be aware of this fact, since when he lived Goku and Vegeta were already dead and Gohan might never told him that.


As Exception from 2:


   Vegeta did this on Namek cause he hated Frieza, he destroyed the planet Vegeta and killed nearly all the Sajyans. (As exception of 2.)


Those are the reasons against, it in my opinion. There might be more, and some might not be right, but I hope you can use this answer.