Sharpen or buy new?

[Moondog55]

After 40 years and quite a bit of use my old centre punch is now blunt. A couple of new ones is only about $35- [ one big + one small] but I'm cheap. Can I sharpen my old one without loosing the hardness that makes a punch leave that nice little cup to get a drill bit started with minimum wandering?
Still no bench grinder tho but my mate works at a school with a full workshop and I thought I might be able to ask a favour

[droog]

Generally hardening is done at a surface level only, depth will depend on the process.
Unless you are removing significant material or cooking the item during grinding there is no issue with re-sharpening a centre punch.
Have re-sharpened mine numerous times.

[r3nov8or]

Take it slow when sharpening, so as not to heat it up, and it'll be fine (also, nothing to lose in giving it a go)