This paper considers the global existence of positive and negative solutions for impulsive functional differential equations (IFDEs). First, we introduce the concept of $\epsilon$-unstability to IFDEs and establish some sufficient conditions to guarantee the $\epsilon$-unstability via Lyapunov-Razumikhin method. Based on the obtained results, we present some sufficient conditions for the global existence of positive and negative solutions of IFDEs. An example is also given to demonstrate the effectiveness of the results.