Can depression make you fall out of love with someone?

Yes. You can lose your emotional tone necessary for connectedness. That is why we do not recommend that people make any life decisions until depression lifts.
Yes. Is is falling out of love or just loss of emotions? Depression can cause someone to lose all positive feelings. While a relationship can be supportive, it can also feel like a burden, when just dealing with one's own life seems overwhelming. I always recommend therapy for both the depressed and the significant other. I also discourage separation until the depression has been treated.