Why do electrons come to ground state even after giving absorbing energy? Imagine you have a hydrogen placed under sunlight, now if we look at 1st shell of hydrogen, it has energy of $-13.6$ev now for 2nd shell we have energy of $-3.4$ev.

1st shell -> $-13.6$ev
2st shell -> $-3.4$ev
3rd shell -> $-1.5$ev
4th shell -> $-0.85$ev
The the continous power from sun is more than enough to send knock electrons out of hydrogen atom, even if we assume the power from sun is not "ample" enough at once, for eg: electron in 1st shell need $+10.2$ev so it can jump into 2nd shell, say sun gives $+5.2$ev at $t = 1s$ so this energy will increase kinetic energy of electron, at $t = 2s$ sun gives $+5.2$ev so electron now jumps into 2nd shell and remaining energy will be used to increase kinetic energy of electron. This process can go on until electron is completely removed from atom?

Why doesn't something like this happen?
 A: There are also other processes that return the electron into the lower energy states: most notably spontanous emission (when electron lowers its energy and emits a photon), but also various kinds of other interactions, such as collisions with other hydrogen atoms. The drive towards lower energy then wins - this is what thermodynamics and statistical physics teach us.
A: To add to @ Roger Vadim's  answer, the different processes also have different time scales, or lifetimes.
You can look at the problem in terms of the different rates at which the different levels are are being filled and the rates at which the energy levels are being de-excited.
If you had a tube of hydrogen sitting in the sun, in equilibrium there would be some number of electrons being excited to an energy level per unit time by the sun, and some number of electrons de-exciting per unit time for each energy. When you have multiple energy levels not only do you need to have an electron in an energy level be available to be excited, you would also need to have a photon at the right energy to give up that energy, so that becomes more unlikely, so the generation rate to higher energy levels become much smaller. If there is an electron in a higher energy level it could have several routes to lose energy, going directly to the ground state by emitting a photon, going to a different energy level, or maybe losing energy to collision or other process.
Also once an atom is ionized unless it is in vacuum and undisturbed it is charged and if there are any available electrons around it will grab the electron, and if occupies an higher level energy state, it will decay down to the ground state via whatever processes are available, since there is a lifetime for that electron in that energy level.
