Kara Danvers has more than earned the name "Supergirl" over the first season and a half of Supergirl. With her super strength, super speed, heat vision, freeze breath, x-ray vision, invulnerability to most human weapons, and flight, many bad guys don't stand a chance against her as long as she spends her time on a planet under a yellow sun. Unfortunately for Kara, it seems that she'll be spending some time under a different kind of star in the second half of Season 2.
The CW has released a trailer that shows a Kara seemingly stuck on a planet beneath a red sun, much like the sun that shone over Krypton before its destruction. Kryptonians like Supergirl and Superman only enjoy superpowers under a yellow sun; beneath a red sun, they're as powerless as any normal person. The Girl of Steel is just a girl when she doesn't have the rays of a yellow sun like Earth's.
Of course, Kara spent the first half of her life on Krypton under a red sun, so she knows how to get by without the powers of flight and super strength. She even temporarily lost her superpowers after a showdown with Red Tornado in Season 1 and had to go about her daily life without the conveniences of her abilities. From the look of things, however, Kara will be in far more danger under this upcoming red sun than she ever was on Krypton or at CatCo. In fact, she'll be bleeding.
Considering how easily she is able to shake off things like being thrown into and through buildings, Kara actually bleeding tends to be a huge deal. The red sun indicates that she's in a kind of trouble that she hasn't yet faced since starting her superhero career. There are a few ways that she could come to be under a red sun, and some are more troubling than others.
The least painful reason for Kara apparently losing her powers is simply that she's stuck in another dream state. When she was attacked by an alien parasite in Season 1, she spent most of an episode dreaming of a life on a Krypton that was never destroyed and that her family never died. She could simply be dreaming or hallucinating of her home again.
Another way that Kara could be bleeding under a red sun is that she has traveled back in time to before Krypton exploded. Time travel is officially a part of the Supergirl universe now that Kara has crossed over the Earth-1 to hang out with Barry Allen and the legends of Legends of Tomorrow; there's a chance that she went back to the past of Krypton for some reason.
A third reason for Kara's de-powering under a red sun could actually have nothing to do with either Krypton or a dream state. Kara may in fact be paying a visit to Krypton's sister planet, known as Daxam. According to Kara, Daxam was rendered unlivable after shockwaves caused by the destruction of Krypton caused solar storms to ravage the land, and she believes Mon-El to be the last surviving Daxamite.
Unlike Krypton, however, Daxam still exists under the rays of a red sun. Supergirl could take Kara and Mon-El to Daxam to investigate whether or not the Daxamites really were all wiped out. Kara certainly doesn't look like she's in the middle of a thriving civilization under the red sun. A desolate Daxam could make sense as the place that robbed her of her powers and caused her to bleed.