I've recently become interested in rex begonias and I've acquired a few different plants over several months.

However, most of them have crispy brown leaf edges. The leaves will germinate and grow just fine but as they approach their final size they get brown edges and die. Some of the leaves have little brown dry spots on them too. A few of my plants only have about 5 leaves, whereas some really healthy ones I just bought (a red planet variety and different one with red and black leaves) have at least 15-20 leaves. It's sad to see the leaves die off before they even reach their full size.

They are sitting in an east-facing window and only get maybe 2 hours of morning sun tops. After that it's just lots of indirect lighting. I make sure to keep the soil damp (not sopping) and I water them when they dry out.

What is killing the leaves off?