Blue Drop/WMG

Hagino is alive!
When the Blue collided with the other ship, their FTL drives collided, creating a space-time anomaly that sent Hagino and Mari falling through time, damaged but alive. This counted as an 'inspiring sacrifice' since Hagino wasn't sure whether it would work and if so even where she and Mari would end up. Both are officially accounted as 'dead', but in reality they're in a better place in a somewhat less rarefied, theological sense. So, where are they now? There are several multiple possibilities:
 * They opened the Door to a New World.
 * They came unstuck in time.
 * They came unstuck the other way.
 * They ended up a hundred and fifty-four years in their past and met samurai.
 * They are Walking the Earth.
 * They Fight Crime.
 * They are students at Seven Moons Academy.
 * They joined the SOS-Dan.
 * They were thrown 1000 years into their future and joined the resistance.
 * They are members of the X-Men.
 * They met a man with a blue police call box.
 * They work for Torchwood.
 * They are a part of section 9.
 * They attend Gakuen Alice.
 * They net battle.
 * They became warriors of the organization.
 * They are players in THE WORLD.
 * They frequent The Time of Eve.

Yui is Hagino and Mari's descendant
Mari and Hagino did This and That, leading to Mari getting pregnant. Yui could be as close a descendant as being their grandchild, since it's indicated that the Arume can become very old, which might also apply to their hybrid offspring.
 * Jossed, Yui's parents are identified in the radio drama.

The Arume actually don't need men for their species to survive
While it is a popular theory amongst some Arume in Tenshi no Bokura, it's shown in the original manga that the Arume are still a fully functioning species 1000 years later with no ill effects even though they still have no men. In that time, it seems they've either found a scientific fix or they've evolved one naturally.

The Blue Drop universe was one of the customers that lost the bid to have Gordon Freeman save it.

 * Dr. Breen let it gleefully slip that Gordon's services were available to "the highest bidder," Combine dominated Earth won it from the Blue Dropverse, whose resident Arume would find a lot of crowbars speeding down the hallway at them.

The Arume do need men for their species to survive, but not right now, or in the near future
Whatever genetic decay makes retrieving Arume men neccesary is ridiculously slow, so much so that they have thousands of years to decide; until then they'll just have a steadily-but-very-slowly increasing rate of genetic disease/problems and congenital birth defects, probably a few tenths or hundredths of a percent per decade, so a thousand years later it still isn't that noticable, and is easily mistaken for environmentally-caused problems; as the problem is so slow to develop, most Arume in the know don't see it as being worth it to change things. Being that those in the know are major leaders, they know that if they do change things they'll face major opposition, because its simply too long-term a problem for anybody to seriously worry about compared to the inherent desire to maintain the status quo.

Eventually- far into the future when peace exists between humans and Arume, thousands of years after even the one-thousand-years-later series, the incidence rate of defects and problems will climb high enough that the populace will get restless and angry and some enterprising Arume politician will bring out the "men" solution and pretend its a new revolutionary idea- it having been kept secret just so they could reasonably try and claim that- and things will move naturally from there to a better ending.