"while not forgetting" is a perfectly correct and usable part of a sentence in written English.
You can use it to introduce a second idea or activity, which reminds the reader of the first one. For example: "I'm taking a break from studying for exams, while not forgetting that I have other important deadlines to meet."
If a team ever needed to look at its issues honestly while not forgetting its strengths, it's the Nats now.
With a son's harsh condescension he spells out Stephen's failings and blind spots, while not forgetting his generosity of spirit.
Whatever the case, while not forgetting the sorrow and pain of Reeva Steenkamp's family, Pistorius is, like Othello, a tragic hero.
If you think taxes are too high, then propose methods of reduction while not forgetting the essential services that tax money supports.
It's hard to be academically focused while trying to make new friends, blend in while not forgetting who you are, and balancing the two worlds.
Blink-182 and Green Day's return ultimately proves pop punk can still shine an uncomfortable torch on society, while not forgetting the power of a well-placed dick joke.
It's a piano in a gin joint, somewhere in the desert, off the stage for a while but not forgotten, and waiting for the next set of hands to bring its old sounds back to life.
The way experienced players keep the drone going is by blowing out while breathing in, not forgetting to breathe in at all.
All the while, Dr. von Braun had not forgotten his dreams of space travel.
And after your kids have been focused on learning for a little while, don't forget to give them time and space to play by themselves, without rules.
While CEOs must not forget to include their senior team in the deliberation process, it should be remembered that the final choice is ultimately theirs.
