In Sipser's book there is a section describing how to decide
$\qquad\displaystyle \mathrm{ALL}_\mathrm{NFA} = \{ \langle N \rangle \mid N \text{ is an NFA}, L(N) = \Sigma^*\}$
in polynomial space. To do so, it shows $\overline{\mathrm{ALL}_\mathrm{NFA} }$ is in NPSPACE.
I don't understand this part: If $M$, the NTM deciding the language, rejects any strings, it must reject one of length at most $ 2^q $ where $q$ is the number of states in $M$. For any longer string that is rejected, some states would repeat. But why? Is there any alternative explanation that helps in understanding this part?