Well... yes and no. On one hand, it could be translated as "śpiący". But the main meaning of "śpiący" is "sleepy", not "asleep". And the vast majority of people would understand it that way unless you provided a very clear context to clarify it.
If a part of your body is 'asleep', the Polish adjective is "zdrętwiały".
Will not accept "His wife is sleeping" and then gives that same sentence as the official translation
And again, a bug. It's strange and kinda worrying that it happened to you twice... at least twice, that's the second such comment that I see.