"No more" is not an unusual thing for anyone to say, especially in sci-fi. I wouldn't take the one instance of Rassilon saying it as being related to the repetition in The Day of The Doctor (the 50th-anniversary episode).
Obviously, the phrase means the same as "enough is enough". It is a declaration that you will not accept something any more. In the case of the War Doctor, it appears that after fighting in the Time War for so long he finally decided that he could tolerate "no more" and made the decision to end it by using The Moment. The War Doctor is seen using a gun to etch the words into a wall which apparently marks his decision.
When The War Doctor encounters the AI of The Moment, using the form of "Bad Wolf" Rose, she repeats the phrase "no more" a number of times in a mocking imitation of him. She does this as part of the AI's attempt to discourage him from using the weapon. It also suggests that the AI is able to see that this phrase (or the decision it represents) is somehow in the War Doctor's subconscious.
The phrase is also one of the titles given to the painting ("Gallifrey Falls", being the other title"), and this is an important plot element because initially, The Doctor believes that both titles refer to the end of Gallifrey at his own hands. He is later told by The Curator that it is, in fact, one title "Gallifrey falls no more", meaning that he successfully changed events and saved it.
So yes - the phrase is used a lot in The Day of The Doctor, but all for reasons of internal logic and plot. Any other uses of it in Doctor Who I would regard as incidental. And yes, your suddenly hearing it after watching DotD is probably an example of Baader-Meinhof Phenomenon.