Why aren't stars like Eternally Collapsing Objects? We know that stellar radiation pressure balances the gravitational compressive forced of a star. Are there other factors which resist such a collapse? Also, if radiation pressure balances gravitational compression, shouldn't the process of shrinking be a quasistatic process making stars Eternally Collapsing Objects (ECOs)?
We know that stellar radiation pressure balances the gravitational compressive forced of a star.


We do not know that. Degeneracy pressure, thermal pressure, and radiation pressure are what collectively balance gravitation in a star. Degeneracy pressure dominates over the other two in white dwarfs and neutron stars. Thermal pressure dominates in low mass stars such as the Sun. It's only in very massive stars where radiation pressure dominates.


  Shouldn't the process of shrinking be a quasistatic process making stars (Eternally Collapsing Objects)?


You are forgetting about fusion. A star is more or less in equilibrium thanks to a number of negative feedbacks. (Negative feedback in a control system is good. Positive feedback is very bad. The "screech!" sound you occasionally hear from microphones is positive feedback.)

Suppose the fusion rate increases slightly in a region near the center of a star. This increases the temperature and thereby the pressure, which in turn causes the core to expand, which in turn causes the density and temperature in the core to fall, which in turn decreases the fusion rate. The reverse applies for a slight decrease in the fusion rate. Similar negative feedbacks apply for changes in temperature, pressure, and density. A main sequence star is self regulating.

Things get a bit trickier when a star leaves the main sequence, but that is a different question.