The student was receiving dual instrument flight instruction. She had conducted several practice instrument approaches, all in VMC conditions. The last was an ILS to runway 13 at Corpus Christi International Airport. It started in VMC conditions but entered clouds at about 550 feet. The descent continued to about 300 feet at which time the CFI called a missed approach. The CFI started a climb to about 350 feet and he felt ground impact. Before impact he noted the aircraft was in a 20 degree right bank and he leveled the wings. The student stated she was in a state of fatigue when the accident occurred. She had been using the airspeed and vertical speed indicators to verify the aircraft was climbing. She made no reference to the attitude indicator for pitch control. The CFI stated he spent 3 or 4 hours with the student doing basic airwork. The CFI had renewed his CFI certificate 3 days before the accident by attending a FAA approved ground training course. There was no flight check involved in the certificate renewal.