How is it possible that gas is stored kilometers deep? Where does all the material on top come from? If new plankton would create more gas, would the new gas be at similar depth in a few 100 million years? And would current reserves be even deeper in billions of years, perhaps 10s or 100s of km deep?
From your question you are obviously aware that gas deposit arise from life forms sinking to the bottom of shallow seas when they die, they accumulate over time and are subsequently covered by marine geological sediments.
Over time the thickness of the sediments increases. As the sediment thickness increases,
The weight of accumulating sediment very slowly pushes the source rock further under the Earth's crust, by a few meters to a few hundred meters every million years or so. This gradual sinking is called subsidence and leads to the formation of sedimentary basins.
I would qualify the above quotation in the source rock is pushed further into the Earth's crust, not under the Earth's crust, as pushing under the Earth's crust can suggest it gets pushed in the the Mantle or the contact region between the Mantle and the Crust.
The surface of the Earth is not static, it constantly moves, via a process called plate tectonics.
Additionally, different types of rock have differing degrees of flexibility and rigidity. Under various ground stresses rocks will fracture and faults and other discontinuities arise. Under certain situations the alignment of such faults can produce graben and horst structures. Horst structures rise while graben structures sink, mainly due to gravity.
Over time, sediments can fill graben structure and over the course of millions of years the original deposit of life forms ends up being buried deeply. At depth, the remains of the life forms are "pressure cooked" - subject to high temperatures and pressures - producing natural gas.
A practical limit to commercial gas/oil drilling is 30,000 ft and generally not much deeper than 20,000 ft. The high temperatures and pressures are difficult to control. There are several mechanical limits like draw works power and casing strength ( commonly 125,000 psi yield steel is used and it is not strong enough for these wells.). It would be much easier to reach methane hydrate deposits on the sea floor if you can figure out how to produce it.