Reserves, proven or otherwise, are just a tally of oil which has been discovered or is inferred to exist within an area where oil has been discovered.
We keep drilling more wells, so we find more oil, so reserves have been keeping up with demand and usage.
At some point, the amount of oil found will not keep up with the amount being used (then prices will really go up, and useage will decline). That is what the whole concept of "peak" oil is about, the maximum rate of possible production.
So far, that peak has been pushed back by better drilling and production technologies, enabling us to recover oil we could not have (economically or otherwise) recovered in the past.
As far as "running out", it sure is a lot harder to find a multi-billion barrel oil field now than it used to be, most were discovered in the 1950's and before.
"At some point, the amount of oil found will not keep up with the amount being used"
You have given no reason to think this must be the case. As more oil is used and more money is made in the industry, more resources are mobilized to finding additional oil. Techniques are improved, searches extended, theoretical understanding increases, etc.
As an energy budget matter, all human energy use is still only a fraction of known, lasting sources of input power (sun and radioactive decays and core cooling etc). The form that takes (mere heat, chemically stored, biomass, the exact mix etc) is an unknown.
And incidentally, the peak oil theory is a claim about absolute production, not production relative to use. And there is no sign to date of oil production declining. It is higher now than it has ever been. Those promoting it rest everything on distinctions among field sizes, which is an inherently murky measure, since it is essential an arbitrary net of distinctions thrown over an amorphous blob of data (are these ten wells in one field or in ten or in five?)
Naturally the easiest stuff to find is found before harder stuff to find. But there is no a priori reason to think the unfound stuff has to be a smaller volume overall. It is by definition unfound.