Associative Property of Convolution:
The proof of associativity of discrete convolution relies on the assumption that multiple infinite sums can be evaluated in any order. This is not true if some of the involved sequences do not converge absolutely, which is the case for the given sequences $x_1[n]$ and $x_2[n]$. Note that the convolution sum $x_1\star x_2$ does not converge, i.e., $x_3\star (x_1\star x_2)$ gives yet another (infinite) result.

In continuous time you have the same problem. Associativity of continuous convolution relies on Fubini's theorem for switching the order of integration. If the assumptions of Fubini's theorem are not satisfied for the given functions, convolution is not associative.