Pelargoniums can live for decades if properly looked after. It sounds like yours has problems at root level and is going from waterlogged to dessicated, probably also lacking nutrients. It may be potbound, or the soil might just be packed down, maybe it is just out of nutrients. So I would suggest repotting with fresh soil as a first step.

You can cut it back. Pelargoniums are pretty good at sprouting from cut branches. They can be a bit picky about sprouting from the old woody stems. Another idea is to take a cutting and grow a brand new plant or three :)

I lost mine to an ice storm in January...they were five years old. I made it a habit to cut them back by about half in Fall to save them from being whipped around and broken in a coastal storm, then cut them back hard (6 - 8") each year in March, followed by adding compost to the top of the 24" container. I would then begin feeding occasionally with Peters, half strength. They were full and huge (3' + across) with two per each container, bloomed wonderfully Apr thru Nov until they met a winter they couldn't survive. Replanted in April, we'll see how long I have these...

I finally fertilized my pelargonium a week ago and now it's blooming! I haven't seen it bloom like this for years..Here's a pic I took today:
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and that's a shot from the back:
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