New approaches named $t^n$-stability of zero effort miss and short-time stability of guidance loop are introduced for analyzing the stability of homing guidance loop which includes the non-ideal missile/autopilot dynamics. In the-stability criterion, guidance loop stability is defined as the monotonic convergence of the zero effort miss to zero which is directly related with the miss distance in the intercept engagement. This criterion is applied to the general homing guidance law and PN guidance law to find stability conditions. The short-time stability criterion is extended to accommodate time-varying state weights and time-varying bounds of the state norm, and it is applied to the PN guidance loop stability analysis. A comparison study of stability conditions based on the Popov stability criterion, $t^n$-stability theorem, and short-time stability theorem shows that the Popov stability condition is most conservative and the short-time stability condition is least conservative. To extend the stability region, the time-to-go freezing technique is introduced. Effects of time-to-go freezing on guidance loop stability is analyzed by using the short-time stability theorem developed in this study. Short-time stability theory is used to determine the time of time-to-go freezing.