Coefficient matrix not invertible with a corARMA model

Question

I am currently working on a project involving the nlme package in R. The acf plots are showing that there is autocorrelation, so I've decided to define an autocorrelation structure by using an autoregressive moving average (ARMA) correlation structure.

I am trying to select the best model of the several models I am running, but I am running into issues with corARMA. Here's the chunk of ARMA correlation models I'm running:

mod2 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=0, q=1))
mod3 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=1, q=0))
mod4 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=0, q=2))
mod5 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=2, q=0))
mod6 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=1, q=2))
mod7 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=2, q=1))
mod8 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=2, q=2))
mod9 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=0, q=3))
mod10 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=3, q=0))
mod11 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=1, q=3))
mod12 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=3, q=1))
mod13 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=2, q=3))
mod14 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=3, q=2))
mod15 <-update(GLS_Mod1.1, corr=corARMA(form=~1|INCUB_YEAR, p=3, q=3))

mod7 is returning an error:

Error in `coef<-.corARMA`(`*tmp*`, value = value[parMap[, i]]) : 
  Coefficient matrix not invertible

mod8 is also returning the same error.

I'm not sure what this means and how I can get rid of this error. Does it have something to do with the p and q?

UPDATE: I have added a mod16 which has a p = 1 and a q = 1, yet it is returning the same Coefficient matrix not invertible error. Is my dataset/time series just too complicated for nlme?