Plant problems

A neighbor gave me a tiny plant when she moved away a year ago. I put it out on the patio to fend for itself over the summer and when I brought it in, it happily began producing buds. In December, it finally bloomed with lovely salmon-tinged yellow petals. It looks good and healthy in this picture.

Since then, the plant has become covered with a white fungus and is dying back. It's still producing a few blossoms but it looks awful. I don't know what kind of plant it is or if this is typical behavior. Does anybody know what's going on with it?

I don't have much of a green thumb but I'm nowhere near as bad as my mother was. It was always a family joke that if we gave her a plant for Easter it would be dead by Mother's Day.

Mom just loved Gloxinias. They had big showy pink or purple blossoms and sometimes she'd buy one for herself at the grocery store. Now the thing she loved about Gloxinias is that after they blossom, the plant dies back. But, if you put it away to "rest", you can restart it to grow and bloom again. As a result, she would store them in her basement but then, forget all about them. There were dried up husks of old Gloxinias in colorful foil-wrapped pots scattered everywhere. She always meant well...

I once gave her a paperback book called, "The Power of Prayer over Plants". She was not amused. We still chuckle over those loving memories of her.