Low pass filter output showing instability
I am going to explain Robert's answer below.

Apply Z-transform to both sides of the equation. You get the following:
\begin{align}
Y(z) [1 - 2z^{-1} + z^{-2}] = X(z)[1 -2z^{-6} + z^{-12}]
\end{align}

The transfer function is given as
\begin{align}
H(z) = \frac{Y(z)}{X(z)} = \frac{1 - 2z^{-1} + z^{}-2}{1 - 2z^{-6} + z^{-12}} = \frac{(1-z^{-6})^{2}}{(1-z^{-1})^{2}}
\end{align}

The denominator represents the poles of the filter $H(z)$. In this case, there exists two poles, both of which lie on the unit circle at $z=1$. For a filter to be stable, all the poles should lie inside the unit circle, i.e., the roots of the denominator polynomial of the transfer function $H(z)$ should lie inside the unit circle.

Perhaps, you can also try a different MATLAB implementation of the above filter:

a1 = [ 1 −2 1 ];
b1 = [ 1 0 0 0 0 0 −2 0 0 0 0 0 1 ];
lp_sig = filter( b1, a1, x );