The phrase "again sinking" is correct and usable in written English.
It can be used to describe a repeated action of sinking or a return to a state of sinking, often in a metaphorical or literal context.
Example: "After a brief moment of hope, the ship was again sinking beneath the waves."
Alternatives: "sinking once more" or "sinking again".
Statistics vary, but the city is again sinking, at roughly a centimeter a year.
"The government is once again sinking so low as to pitch one group needing the community's support against another," she said.
In February 1941, Admiral Hipper sortied again, sinking several merchant vessels before eventually returning to Germany via the Denmark Strait.
Just as America was yet again sinking into spiritual sluggishness, a Third Great Awakening seized the nation.
But, with all the attention being paid to McChrystal's ouster, this news also appears to be (once again) sinking like a stone in the American media, leaving few (if any) ripples in the public's awareness.
My period of playing and enjoying RPGs was over; I would return to just playing FIFA and be done with it, never again sinking 100 hours into something or caring about the fretting shrieks of an adolescent girl (who also has The Magic That Can Save the World, or something) while a pervy old man and a talking salamander make awful jokes in the background.
This week the euro once again sank against the dollar.
Prime minister's questions had once again sunk into a limp stalemate.
Again, they revealed themselves as a team of some depth, and into it the Giants once again sank.
A feisty Mr. Santorum once again sank his teeth into a rival later in the debate, accusing Mr. Perry of having supported the bank bailout known as TARP with a letter to lawmakers on the day they voted in Congress.
The Millennium Development Goals will need to be revised, as many households again sink back into poverty and as many, and more, remain mired there.
