I have exactly one permanent marker, a small keychain-sized one called the Sharpie Mini that works well for marking plastic freezer containers.
The last time I went to use it, it was laying in the kitchen drawer with the cap off. Not sure how that happened, but I'm just gonna blame the cat.
The keychain Sharpie was dead. It refused to write.
It wasn't that old and hadn't seen a ton of use, and it was the only one I had, so I turned to the collective wisdom of the Internet to fix it.
The general consensus was that when a permanent marker dies, it usually still has ink in the reservoir; the tip has just dried out and lost its absorbency.
The most common solution: For markers that use alcohol-based ink, add rubbing alcohol (surgical spirit in the UK).
I found the simplest instructions for reviving a Sharpie on the the official Sharpie blog, attributed to Karen from the The Art of Doing Stuff site.
The instructions were to pour a bit of rubbing alcohol into a bottle cap, then place the tip of the dried Sharpie in the alcohol. Leave it long enough to see a ribbon of ink flowing out.
Then recap the marker and let it sit for 15 minutes.
The idea is that leaving the marker uncapped allowed all the alcohol to evaporate from the porous tip, causing the dried ink to clog it up. Adding alcohol rehydrates the ink and loosens it up, and the porous tip once again draws ink down from the reservoir.
(Others have suggested using vinegar or fingernail polish remover – acetone – but I don't know how effective that is).
Now, I didn't have any rubbing alcohol, but I did have a whole box of alcohol pads. Long story short, about 50 alcohol pads later, my Sharpie returned more or less to life, but didn't work as well as it had. Probably would have had a much better result using actual rubbing alcohol.
There are more complicated ways to rehydrate your Sharpie.
Crazy Russian Hacker shows in this video how to remove the ink reservoir from the barrel, then add alcohol 4ml at a time using a dropper.
Another technique I've seen people recommend is to stand a Sharpie point up and use a syringe to inject alcohol directly into the tip.
If you try either one of those methods, just remember to add alcohol a little bit at a time until the marker starts working again. Too much alcohol will completely dilute the ink and you could end up with a mess.
Also, be careful of your fingers when using pliers or needles.