Everything you put in the research machine is gone for good: the challenge of this game is to survive with the limited resources you have available.
Here's a handy list of the current known resources and their availability:
- Berries: infinitely renewable in the wild. If dug up and replanted, renewable but must be fertilized after every five berry harvests.
- Manure: infinitely available, as long as you have a herd of beefalos near you, or a pigmen village;
- Beefalos: renewable. Calves are born every autumn which add to the herd.
- Pigmen: generated indefinitely from their village.
- Wood: renewable. Trees can be planted back from pine cones, unless you destroy the pine cones or burn the forest. Pro tip: dig up the tree stump to get one more log;
- Gold: renewable. Gold from gold-veined boulders don't respawn, but if you find a Pig King you can feed him meat (a renewable resource) or other items to get gold nuggets in return;
- Flowers: renewable. Flowers spawn butterflies which, when caught with a bug net and planted, yield more flowers
- Spiders: putting them in the resources because of the Silk. The nests generate new spiders when you kill them, up to their current limit (it should be 6 for the small nest, 9 for the medium and 12 for the big). Spider nests themselves can be "planted" with spider eggs, that are obtained when destroying a big nest (and maybe also from a medium nest);
- Rabbits: my guess here is that they're regenerated as long as their holes are intact (you can dig up a rabbit hole to force them out);
- Turkeys: they're vermins and they're there to gobble on your berries! Randomly generated in any bush, you don't have to worry about their quantity.
- Flint: Those that you pick up don't respawn anywhere else on the surface. They respawn in a cave when it gets regenerated;
- Rocks: Destroying a boulder or a stalagmite yields rocks, flint and occasionally gold, but boulders don't respawn. Stalagmites are regenerated with the cave they're in if you choose that option at the cave entrance;
- Frogs: they appear to be continuously generated from ponds. Frog Legs are also left when a Merm is killed.
- Fish: appear to be continuously generated from ponds. Fish are also left behind when a Merm is killed.
- Carrots: more research is needed. When you pick them you cannot replant them, but it looks like they can spontaneously appear in random spots of the map. (Of course, you can also grow carrots in farms.)
- Saplings - once they're gone (e.g. by being burned), they're gone
- Berry Bushes - likewise
- Grass Tufts - likewise
- Rabbit Holes - if you dig one up, it's gone forever
As you can see, the list is still a work in progress, since I'm trying to discover everything on my own. I'll try to keep this updated every time I find something new. Keep in mind anyway that new features are constantly added to Don't Starve, so these information is not fixed and still likely to be changed from time to time.