It's a little bit of both. Human mages can generate magical energy too, by converting their own life force, but our spells won't activate in the first place without interacting with the mana in the world around us.

[She raises a finger.] You know how you can't have fire without oxygen, right? It's exactly like that. We're providing the fuel, but without the world's energy to create that chain reaction, we can't make any explosions.

[That's imagery she hopes Tabby can appreciate, because Rin also enjoys blowing things up. Both figuratively and literally in this case; the girl does love her exploding gems. But anyways:]

Both resources replenish, but at different rates. It might take only a few days or hours for humans to generate more mana, depending on how much has been used, but the world replenishes its energy more slowly, as best as its able.

If too much was taken from it all at once, then yeah. It really could be gone forever. It's happened in other worlds.