Hourglassing means that your elements deform in an unrealistic way, which can occur when you use reduced integration elements (for instance S4R instead of S4 in case of shell elements). Usually your deformations become (much) too large as a result of hourglassing.
The hourglass control settings in the element type selection window can be used to prevent bad effects from hourglassing.
Im not expecting that those settings will have much effect on your convergence.
What model are you running ? Describing that would help to understand the reason of convergence issues.