In 1928 Hazlett received a Guggenheim Fellowship that allowed her to spend a year visiting Italy, Germany, and Switzerland. While in Italy she presented a paper called "Integers as Matrices" to the International Congress of Mathematicians in Bologna. Near the end of her visits she requested an extension of her Guggenheim Fellowship, which was granted and allowed her to spend another year in Europe. When she finally returned to the University of Illinois in 1930, she was promoted to associate professor and received a pay raise. However, her teaching schedule was rigorous and required her to teach service courses to large classes of non-math-majors, and after 1930 she did not publish any more research papers. In 1935 she wrote to the chair of the mathematics department complaining that the service courses left her no time for research, but her teaching schedule was not changed and by December 1936 she took a sick leave after having a mental breakdown from the stress of her job. The sick leave was supposed to end in August 1937, but her health had not improved enough by this time and she took another year off. She was, however, able to return to teaching by the end of 1938.