The energy-time uncertainty tells us that if energy uncertainty is zero time uncertainty is infinite. Now for a higher energy stationary state energy spread is zero so accordingly its average life time i.e. time spread should be zero, but higher energy states are less stable than ground state. So its average life time is finite. My question is what is contradicting the time-energy uncertainty relation?
There are multiple reasons for the broadening of spectral lines.
The one you are referring to is what is called the natural width, and it varies for atomic spectra, for molecular spectra, and for nuclear. It is actually due to the fact that those energy states from and which they jump are not infinitely stable. The do have natural half life, so called lifetime, tau, which then through Planck's uncertainty principle determines their line widths. It is to be expected, higher energy levels will over time have a tendency to decay to lower levels. They are not perfectly stable.
There's other factors. They can also have their widths broadened by other effects, such as collisions and Doppler effects. Those can sometimes be much bigger effects.
You can google a lot of writings on this. I found a few, but keep loosing the links in my iPad. See one at http://www-star.stand.ac.uk/~kw25/teaching/nebulae/lecture08_linewidths.pdf
For spontaneous emission, i.e., the natural line width, you can not explain it from Schrodinger's equation and classical QM, which takes the nergy states as infinitely stable. You need to include the effect of the virtual photons around, in essence you need QED. See a little more in https://en.m.wikipedia.org/wiki/Spontaneous_emission