My water heater is now about 15 years old and does a decent job of heating the water, but is is located quite a ways from my shower, and water pressure is getting lower and lower with every passing week. I have never actually drained the water heater of all the water as recommended. COuld this be one of the problems. Would replacing the water heater correct the low pressure issue? Thank you all.

There are many possible causes for low water pressure. Are you on a well or city water? Are there any filters between water origin and water destination? I am assuming your water heater is gas fired; electric water heaters won't last that long. In any event your water heater is living on borrowed time.