How often should elderly loved one's be required to shower?

I would say 1-2 times a week is appropriate. More if there are bathroom "accidents" or spills during eating. It also depends on the climate. If you live in a dry climate, the skin drys out so easily. As we age our skin becomes thin and even tears. I have the person who bathes Mom put cream and powders on her skin right after showering to lock in the moisture and keep the skin pliable. It also makes her feel good and smell nice. The little things count!

My relative is afraid to get into a shower, so her caregivers give her a sponge bath every other day.

Long term care facilities typically shower residents 2 times a week, sometimes only once. My mom is at my home and she would like a shower every day. As long as there is not an odor or skin problem there is not a mandated number of showers required. Showering is a good way to make sure there is no skin breakdown. Lots of older people resist bathing, reminds me of the 8-11 year old stage. Good luck.