I'm still happily using a non-stick frying pan that I've had for almost 4 years.
I only use Teflon utensils.
I never use harsh abrasives.
After cooking, I fill it with boiling water, let it soak for a while and then wipe out with paper towels. Most of the time I just give it a quick rinse and it's ready for the next time.
And buy quality - "Quality is remembered long after the price is forgotten".
I have a ceramic-coated pan too, and always treated it with care (plastic utensils, no overheating, etc.) It failed too, after some time (I think I've had it for 9 months now, and used frequently).
Unlike a failed Teflon pan, it does not look or feel any different. But while at the beginning it was superslick, with everything gliding right off it in a fluid motion, now it is only moderately non-stick. I can still use it as normal, including for such problematic cases as omelets. But if I fry without fat, I need a spatula to dislodge the omelet from the surface. In contrast, when I bought it it was like polished ice. It is still more non-stick than, say, enamelled or seasoned iron, and definitely better than stainless steel. But it isn't as good as a good-quality PTFE.
If the non-stickness keeps at this level, I still think that it makes sense to buy it, if you have the money. They are expensive, especially the brand-name ones, but can give you nice, even heating. While they will give you less non-stick performance, they are more robust than PTFE - metal utensils don't damage them, they don't overheat as easily - and I found the non-stickiness sufficient. The nice thing about them is that the quality ones aren't thin aluminium, mine has a 10 mm sandwiched steel bottom - you don't get this in PTFE. So they can be used for applications impossible with PTFE, and will give you a better heating in the cases where PTFE would have worked.
On the other hand, you can decide to go traditional, with a combination of PTFEs for the sticky applications and iron or steel for everything else. It will probably give you a better tool for the stickies, as long as the PTFE coating itself doesn't fail through accidental overheating. It is up to you which style you prefer, but the ceramics aren't the panacea they are touted as.
Best Answer
There are two different substances that are known as "ceramic nonstick". One is a coating of ceramic material and silicone, offered as an alternative to PFTE (Teflon), and the other is actually a PFTE coating with tiny ceramic "buttons" that protects the PFTE against abrading off when you use metal utensils.
For either coating, one possibility is that you're not actually scratching off the coating. Instead, your plastic utensils are themselves scraping off tiny bits of plastic from their edges on the ceramic material and leaving a "smear" of plastic on the pan. This is similar to scraping the edge of an American dime on granite; it leaves a mark, but that's the metal scraping off on the stone, not the other way around.
The way to verify if that's the case would be both a touch test of the "scratches", and trying some utensils made from other materials (like wood or fiberglass) and see if they also leave marks.
The second possibility is that your plastic utensils in fact have fiberglass, bamboo fibers, or something else extremely hard in them. This could actually scratch the underlying nonstick substance (PFTE or silicone), which is quite soft, especially if the plastic untensils consist of something like fiberglass encased in relatively soft plastic.