Just because it says 50%, doesn't mean it'll succeed once in two tries. I have a feeling you just ran into some really bad luck. As already said, use Sinestro and the Lucky Coin and you'll get a 90% chance. It still could fail though.
Well, I started this post as a rant about "really bad luck" and "once in two tries" (I actually tried probably 50+ times) but I always test my assumptions before hitting post reply and I had to erase all I wrote and start over.
Since I posted before, I gave up trying to capture Supergirl and played a few days more. I upgraded the Legion Hideout to level 2 then went to bed. Today I started up to test how many days it would take to capture Supergirl... and I got her the first try with Livewire and the coin at 60% chance. I then reloaded and tried a few more times, The level 1 villains always failed and the level 2 villains mostly succeeded.
I tested 20 tries for each of the level 2 villains without the coin:
(Name @ stated % = actual % # each try 1success 0fail)
Livewire @ 50% = 85% # 11111111111011100111
Star Sapphire @ 50% = 60% # 10111001110111001010
Toyman @ 20% = 45% # 11110001000001010110
I also tried the other villains but when Shade at 40% failed 100% of the time I didn't bother finishing the rest
Mercy @ 0%
Tala @ 0%
Giganta @ 10%
Atomic Skull @ 10%
Cheetah @ 20%
Shade @ 40%
If you try capturing Supergirl with a level 1 device it tells you "Supergirl requires a level 3 device to capture."
I would add "This villain is not strong enough to capture Supergirl." for the level 1 villains.