Otonashi came to the afterlife presumably much later than Kanade. So she must've received his heart waaaaaaay before he died. And I don't know about you, but I personally need my heart to live for longer than a minute, let alone days, weeks, months or years.
The only almost feasible explanation is that time moves much faster in the afterlife. But even then, IRL Otonashi would've been dead before Kanade received his heart. So that explanation only works if Kanade ended up dying while the doctors were in the midst of removing Otonashi's heart, so really she would've never actually had his heart successfully transplanted into her. And really, the doctors would've realized she's dead and never even attempted to transplant the heart as they would've already known it would be unsuccessful. So she never physically received his heart inside of her, plus she would've had to know who her donor was pre-op. And frankly, that's not likely something you'd know beforehand... It's not as if you're given advance notice that someone's going to die and will be donating their heart to you. It's more like "Holy ****... a heart's available, you need a heart, GOGOGO! QUESTIONS LATER!"
