Maxseek (205): error: G0058: index out of range

This is because when you add another AR term, you also need to add an additional starting value to the variable th in the procedure startval, which begins around line 55 of the file Maxseek. In the original file, th is a 13x1 vector. The comments around line 37-43 tell us what each of the elements of the th vector represent:

//------ Input initial values for parameters ------------
/*   The order in which variables are represented is as follows
              constant term in regression
              autoregressive terms in regression
              initial variance parameter
              constant term in ARCH equation
*/

So before you added the third AR term, the first element of th was the starting value for the constant term in the regression, th[2] and th[3] were the starting values for the autoregressive terms, th[4] was the starting parameter value for the initial variance parameter, etc.

To add a third AR term, you need to add an additional starting value to th between th[3] and th[4]. This value should be as close as possible to the final answer--put in your best guess. Assuming that we thought 0.1 was a reasonable guess, we would change th from the original (below):

      let th[13,1] =
     0.35080500       0.25003200      -0.56817500
     0.027988000      -0.11706300
     11.4016   0.051132  10.765493  0.1208310
       4.3512660        13.146594       0.42415600       -5.2199370 ;

to this (notice the added 0.1):

      let th[13,1] =
     0.35080500       0.25003200      -0.56817500 0.1
     0.027988000      -0.11706300
     11.4016   0.051132  10.765493  0.1208310
       4.3512660        13.146594       0.42415600       -5.2199370 ;

This is in addition to changing karch to equal 3 on line 29, which I think you already did.