Harvesting does not imply a resource is renewable. Most crops are annuals, and we eat the parts needed for reproduction, or harvest them before maturity.

That said, I'm not sure if "renewable" is the right word. On Earth, the water cycle purifies water through evaporation and ground filtering, but not quickly enough for human use, so we process our wastewater and distill our drinking water. On Mars, the environment is not suitable for a water cycle (too cold, not enough water, atmospheric losses), so any captured water should be processed and reused without release.

Your terminology is wrong, you should probably change your question to “is water on mars a renewable resource?”

To way oversimplify: it's finite so you'd eventually have no water to pull out of Mars. However, once you have it and use it, you can try to capture and filter and reuse, and you'd be able to get many gallons of use out of a single cup (not all at once, just cumulatively). But if it somehow escapes, it's gonna get smacked by solar winds and you won't be able to recover those molecules, so you'd want to figure out a good setup to contain whatever water you found. It's that lack of atmosphere that'd cause all the issues, once it leaves your setup it's gone

No, Mars lost 99.999% of all of it's water. The part that remained is stored frozen inside. As soon as you take it out, it will be gone forever.

You can try and use and recycle it as much as you can, but once you lose it, it's lost.

You would have better luck hitting Mars with comets and meteors. The meteors to bulk up mass and (maybe) restart the core and the comets to add water.

I’m not sure how it would be harvested but I guess both would be possible