my gut would say its not a houseplant.. and you might be doing as good as you can ..

but my gut sasses me all the time.. so who knows if he is laying to me..

anyway... were are you.. big city name.. and was the furnace blowing dry air all winter??... keep in mind.. by the time you see the damage.. the cause may be long gone... how cold was it outside.. when you brought it home in february.. and how was it protected...

ken

It's a Rex Begonia, Ken, a popular house plant. The problem is hard to see in the photos but I wonder if it is Botrytis. This might be more than you want to know about them but it has a section on care.

Rex Begonias

Another factor that can cause leaf tip burn is water quality. Water pH, dissolved minerals such as chlorine or fluoride, etc., can all cause problems for plants. Also, if you don’t properly water on watering day, fertilizer salts in the potting mix can cause tip burn. We encourage thorough watering in order to flush out those concentrated chemicals.

Also, if the soil is getting literally all the way dry, there will be repercussions. If you have the opportunity to move it to a clay pot, you might be as pleased with the results as my Begonias have been. The breathable clay allows the soil to stay as moist as a Begonia enjoys while drastically reducing the risk of overwatering (root rot due to lack of oxygen.) I won't use plastic pots for Rexes anymore because of the dramatic improvement in the clay - except one that has a wick.

Another thing you can do is propagate some leaves, so you're not counting on just 1 root system. A healthy Rex leaf stuck in water will almost always make roots. When you see a little poof of roots, bury them just under the surface with the rest of the original leaf secured in some way from blowing around. New baby leaves should start to grow where the roots are soon. For this delicate situation, I use a gentle spritz with a spray bottle to water until the roots are holding the soil in place after a while.

Try increasing the humidity and reducing the watering. Easier said than done!

It could be due to over-watering, lack of light or maybe underwatering. It's hard to say without knowing the exact conditions. Why don't you try giving your plant a bit more indirect light and/or reducing the amount of water per week.