ok this is my opion but wouldent the sun be like lets say a gl ring. the ring has a 24hr time on it so you can use as much energy as you want within that 24hr limit(i believe it was hal jordan who did this once).
its just on a higher scale. superman has no limit on how much he can absorb and the sun will keep feeding him energy.
the sun is like the ring in a since it will burn and produce unlimited energy for superman within a certin amount of time. (the sun will continue to bur for a certin amount of time.)